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.
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