For special occasions, I use my grandmother's recipe for brioche rolls. This sandwich was made with rolls purchased from a French bakery.
2 strips bacon, optional
1 tablespoon butter
1/4 teaspoon each: coarse salt, Creole-style or or other coarse mustard
Freshly ground pepper
1 tablespoon milk
2 toasted brioche buns or 4 pieces toast
Place bacon in a cold cast iron skillet. Set heat at medium. Cook, turning occasionally, until crisp, about 4 minutes.
Meanwhile, whisk together the eggs, salt and pepper. Whisk in milk. Set aside.
Transfer bacon to a paper towel to drain. Set aside. Pour out all but 1 teaspoon bacon fat, if using. Add 1 tablespoon butter.
Add eggs to skillet over medium heat. Cook, pushing and fluffing the eggs with a spatula as they set. Remove eggs from heat. Transfer to bottom half of bun; top each sandwich with a bacon slice, if desired.