Eggs Rothko - cooking recipe

Ingredients

2 tablespoons butter, divided
2 slices brioche bread or 2 slices challah
2 large eggs (extra-large)
2/3 cup cheddar cheese (good quality, grated)

Preparation

Place oven rack in lowest position.
Preheat oven to broil.
Melt 1 tablespoon butter in a large non-stick skillet over medium heat until it begins to foam.
Place brioche slices in the skillet, moving them around until well-buttered and browned.
Using a cookie cutter, biscuit cutter, or drinking glass, press a hole in the center of each bread slice; discard the cutout rounds.
Divide the remaining tablespoon of butter between the 2 holes in the bread.
When butter begins to foam, crack an egg into each hole.
Cook until the egg whites set about halfway up the sides of the yolks.
Flip the bread with a spatula and cook for another minute or so.
Remove bread from skillet and place onto a broiler pan.
Spread grated cheese thoroughly over the bread (covering as much surface area as possible to prevent the bread from burning).
Place pan under the broiler.
Remove as soon as the cheese melts.
Serve with broiled tomatoes or a simply dressed green salad BUT I would want some bacon and fruit added to feel well-fed. :-) .