May a motion court grant relief to a cross movant who requested relief only in its opposition papers to a motion without having filed the formal notice of cross motion prescribed in CPLR 2215? If the motion court denies the sought relief, is that denial appealable as of right, by leave?

This question may seem trivial in light of case law that “[t]he failure to give proper notice of a motion deprives the court of jurisdiction to entertain the motion and renders the resulting order void,” Citimortgage v. Reese, 162 AD3d 847, 848 (2d Dept 2018); Amaral v. Smithtown News, 172 AD3d 1287 [2d Dept 2019] (the failure to provide proper notice for motions “is a jurisdictional defect that deprives the court of the authority to entertain a motion for leave to enter a default judgment”); “this well‑settled rule [of notice requirement] ensures that the opposing party has an opportunity to respond with admissible evidence and pertinent legal argument and precludes appellate consideration of issues ‘if proof might have been offered to refute them had they been presented in the [trial] court.’ ” Arthur Brundage v. Morris, 174 AD3d 1088 [3d Dept 2019].