Brown bacon in a 12-in. cast-iron skillet over medium-high heat, 8 to 10 minutes, turning as needed. Transfer to paper towels and drape with foil to keep warm. Discard fat from pan and wipe pan somewhat clean with a paper towel.
Meanwhile, cut 4 brioche slices, each about 1 1/4 in. thick (you'll have bread left over). Spread both sides with about 3 tbsp. butter total. Cut a hole in each slice; set centers aside.
Put bread in pan, pressing down slightly to flatten, and set over medium-low heat. Put about 1/2 tsp. butter in each hole, then crack an egg into each. Sprinkle eggs with a little salt and pepper. Cook until bottom of bread is golden, 3 minutes.
Flip toast and eggs carefully with a wide spatula. Sprinkle eggs with salt and pepper. Cook until underside of toast is golden and egg is done the way you like, about 3 minutes more for softly set.
Transfer eggs and toast to plates. Quickly toast bread centers, then set 1 on each serving. Serve with bacon.
*Find at Trader Joe's and other well-stocked grocery stores.