Dad's Eggs Benedict

Lest you be fooled, this is not your ordinary Eggs Benedict. But, it is better!
Dad's Eggs Benedict
1 pkg Bran Muffin mix
4 tbsp flour
4 Tbsp butter
2 C milk
Cheddar cheese, shredded (at least 1 C)
Bacon
Eggs (1-2 per person)

Mix and bake bran muffins according to package instructions.
Make sauce: Melt butter in a sauce pan. Add milk and flour to a jar, shake to combine. Pour milk mixture in with melted butter. Stir constantly until thickened. Add cheese to taste, and stir until melted.
Poach eggs in a shallow pan of boiling water. 3 minutes for soft centers, 6 minutes for hard.
Cook bacon.
Split muffins in half. Layer on plate: muffin, bacon slices, eggs, and sauce.