The Panel for Educational Policy has struck down New York City’s school funding formula — breaking with City Hall directives for the second time in two months.

Officials from the Department of Education raised concerns that the panel’s Wednesday night vote could delay school budgets and preparations for school reopenings in the fall.

“This is deeply problematic, but the vote has been cast,” said Schools Chancellor David Banks. “We’re going to have to figure out a much better way in which we work together.”

The 15-member education panel — made up of nine appointees by Mayor Eric Adams, five by borough presidents and one by parents — has previously garnered the reputation of a “rubber stamp” for City Hall policy.

But with a slot vacant after an Adams pick with a history of anti-LGBT writings resigned, the panel lacked the mayoral-appointee votes to push the current approach to school budgeting through — sending the 15-year-old formula, which gets re-approved each year, back to the drawing board.

“Will there be some disruption? Absolutely,” said Vice-Chair Tom Sheppard, who represents parents on the panel, as he voted “no” on re-approving the current formula. “In the long term will we address the needs of our students? Absolutely.”

Members of the panel and public noted that while the formula sends additional funds to schools serving kids struggling on state tests, learning English or those with disabilities, it lacks weights for other vulnerable students, including those who are homeless or in foster care.

“If we’re holding each other accountable, everyone needs to be held accountable — DOE as well,” said member Geneal Chacon, the Bronx borough president appointee.

Just last month, the PEP voted down a $82-million temporary staffing agreement, used by the DOE’s central office and school administrators to employ workers for short-term initiatives, like COVID-19 response teams. Watchdogs said it was just the second contract to be struck down in the panel’s history.

After further discussion, the contract got the green-light on Wednesday.

The PEP has rarely struck down mayoral directives. But the unusual, two-time rejection of City Hall directives raises the possibility this panel could usher in a new era of checks on the administration’s power — while the state debates the extension of mayoral control over Big Apple schools.

Lawmakers have told The Post that several options are on the table, whether a multi-year or shorter extension of mayoral control, or changing the makeup or rules of the PEP that would give it more autonomy to respond to the mayor.

Adams’ predecessors have insisted that panel members fall in line with their policies — with former mayors Michael Bloomberg and Bill de Blasio even axing dissenters.

In non-pandemic times, the DOE releases school budget allocations in the late spring, so that principals and administrators can propose plans for the coming year in June. But over the past couple of years, the allocations have come late, with DOE officials citing difficulties related to COVID-19.

“We are disappointed in the outcome of this vote, and it will potentially delay school budgets and preparations for the upcoming school year,” said Nathaniel Styer, a spokesperson for the DOE.

“We are committed to a full review of the Fair Student Funding formula, but that review, for the sake of our students, cannot be rushed in a matter of weeks or months — it must be a thoughtful review,” he said. “We are expecting the panel to come back to this issue in order to prepare for the upcoming school year.”