Why can the middle of a cake collapse while the edges look baked when the same batter is baked in a deeper pan?

Answer: Center heats too slowly

Center heats too slowly ✓ — Right: pan geometry changes the heat path. A deeper cake has more batter for the same exposed surface, so the center reaches starch-gelling and protein-setting temperatures later than the edges. The outside can pass visual tests while the inside is still too weak to hold expanded bubbles. That is why pan size is not cosmetic; it is part of the recipe.

Top has too much steam — Steam at the top is not the main issue in a deeper pan. A thicker mass gives the center less exposed surface area relative to volume, so heat arrives late. Steam can help lift batter, but the center still needs enough time near setting temperature. Too much attention to the top hides the underbaked core.

Edges prove it is done — Edges are useful clues, but they do not prove the center is done. They are closer to the hot pan and oven air, so they brown and firm first. In a deeper pan, that perimeter can look finished while the core is still a weak gel. The misconception is trusting the fastest-heating part to speak for the slowest.