Create a rue by melting flour and butter together in a saucepan. Cook for one minute and slowly start adding milk to the rue. Cook over medium heat, whisking to make sure the sauce doesn't scorch, till sauce thickens and begins to boil.
Decrease heat and add cheese. Stir until cheese is completely melted and remove from heat.
Using a 1.5-quart casserole dish begin by layering a thin layer of sauce followed by eggs and then bacon. Repeat at least twice. End with sauce followed with a bacon top.
Bake on 350 for 20-25 minutes, until casserole is bubbling.