Preheat broiler. Place 8 slices brioche on parchment-lined baking sheet. Top each of 4 slices with ham.

Top all slices with 3 tablespoons bechamel; spread evenly with a knife.

Top all slices with 2 tablespoons grated cheese.

Broil until cheese is bubbling and light brown, 10-15 minutes.

In fry pan, cook eggs sunny-side up. Stack the 4 slices without ham onto the ham-topped slices.

Top each with 1 egg.