“Regular order” is a parliamentary term getting bandied around plenty these days. Mostly it’s being invoked wistfully by lawmakers convinced they’d be able to triumph over legislative stalemate and partisan discord if only Congress would play by the formal and informal rules of the good old days.

The concept is getting cited by frustrated Senate backbenchers every time there’s another balky interlude in the immigration debate. In the House, leaders in each party are blaming the farm bill’s defeat on the other side’s failure to abide by the principle.

But no single lawmaker has pledged fealty to the phrase more forcefully than Barbara A. Mikulski, who’s made “a return to regular order” her motto and her professed goal since taking the gavel of the Senate Appropriations Committee this year.

How the Maryland Democrat defines the term started to come into view Thursday. That was when Mikulski marked a milestone in congressional history, becoming the first woman to preside as one of the annual spending bills was debated by one of the Hill’s two Appropriations panels.

The most basic job of Congress is exercising its power over the purse, which is supposed to happen by enacting a dozen bills a year to apportion the one-third of the budget over which it has annual discretion. But the process has broken down so thoroughly that none of those individual spending bills was passed by the Senate in four of the past six years, since Democrats took the majority.

The overwhelming conventional wisdom is the process is already pointed irreversibly toward another deep ditch. Mikulski insists she’s still got a shot at changing that. If so, it will require insisting on regular order when it helps her and skirting the system when it doesn’t.

Her boldest move Thursday seemed to fall squarely in the latter category. She pushed through a grand total for the fiscal 2015 spending bills that ignores by a country mile the spending cuts mandated by Congress in the debt and budget law of three summers ago. The Mikulski  figure is $1.058 trillion — 9 percent, or $91 billion, more than the cap mandated in that 2011 law, which is the total that majority Republicans in the House have promised to live with. (Their amount is $967 billion, or 2 percent less than what’s being spent in the current year.)

Mikulski said the larger figure was required of a Congress that wanted “to be frugal but not heartless.” The new top Republican on the panel, Richard C. Shelby of Alabama, countered that appropriators “must be guided by the law as it currently stands.” And besides, he said, spending above the limit now would only deepen the potential pain in the end. Absent a bipartisan deal to turn off the sequester, the White House would be required to apply an across-the-board axe even more deeply than the cuts happening this year

Score one for regular order and against Mikulski, or so it seemed.

But then Shelby called for something that stumbled over his own rhetoric. He proposed having the Senate hew to the smaller number while abandoning the firewall that’s supposed to apply the spending pain to defense and domestic programs equivalently for the next decade — a central element of the punishment Congress imposed on itself for not being able to come up with a deficit reduction deal by the end of 2011. That was also an improper deviation from the rules, Mikulski and her allies said, which would end up applying an even stronger sequester to the Pentagon than what’s on the books.

Shelby’s plan was put down, 15-14; round two in the battle to define regular order had gone to the chairwoman.

And then she easily triumphed in the final two matches of the day — arguably, the most important ones. She won approval of the year’s first two bills, $20.9 billion for agriculture programs and $74.4 billion for veterans programs and military construction, with the sort of bipartisan votes few chairmen can dream of in Congress these days: not only all her fellow Democrats, but also a majority of eight of the 14 Republicans.

Mikulski says her next regular order goals are to finish the dozen markups in July and “actually, actually try to get bills on the floor” before the start of the August recess.

That’s an extremely tall order, given all the complicated procedural and political traps in her way and the signs from senior Republicans, such as Shelby, that they’re ready to drain some of the customary bipartisan bonhomie out of appropriations work. But Mikulski is showing she’s not always going to run things the same way as the 27 men who preceded her since the committee’s creation just after the Civil War.

She showed a glimpse of that last week, suddenly suspending a tense hearing on cybersecurity in order to respond to a critical comment on Twitter by BuzzFeed reporter Rosie Gray, that  “@SenatorBarb is trying hard” to limit the scope of the questioning.

https://www.youtube.com/watch?v=4oiTUcKUpYM

Not so, Mikulski said, and 17 minutes was as long as she was willing to wait before firing back. And then, in a moment that’s gone a bit viral on social media, the 76-year-old senator waved her smartphone aloft, looked into the TV cameras and said: “So, Rosie, it’s an open hearing. Hi. Look forward to keeping in touch.”

That’s the sort of new twist on regular order that might be needed in order to untangle the morass Mikulski’s confronting this summer — and in a way that permits her to credibly claim she’s been true to her word.