Two connected pawns on the seventh with their king in front can even win against a queen. The queen's side holds only by pinning one pawn and preparing to trade the queen for the new queen.
A reversal of roles: White has the queen but must fight for a draw. Black's pawns stand on d2 and e2 with the king on e1, and White's king on h7 is useless. If White makes a random move, Black promotes one pawn with the other protecting it, and the resulting queen-plus-pawn versus queen position is lost for White because the black king is sheltered.