Use a 3-inch cookie cutter to cut a shape out of each piece of the bread. Assure that the bread is uncut around the edges so that the egg stays inside the hole.
Drain the peppers.
Melt butter in a large skillet or a griddle.
Place bread and cut-out pieces inside skillet, and toast them on the bottom. Turn all bread pieces over.
Break an egg into each hole with the pieces of bread.
Add a strip or 2 of red pepper to each nest.
Season the eggs with salt and pepper and sprinkle a little cheese into each nest.
Cover the eggs with a lid. They are perfectly done when the whites are firm and the yolks are just glazed over.
Transfer to a platter, sprinkle with fresh basil and serve with the cut-outs.