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1
Butter one side of each slice of bread, and place on your work surface, buttered side down.
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2
Using a 2 1/4-inch-diameter glass (such as a juice glass) or a sharp knife, cut a hole in the center of each bread slice.
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3
Press the cheese evenly onto 4 bread slices around the hole.
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4
Place the remaining 4 bread slices on top, buttered side up.
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5
Heat a large nonstick skillet over a medium-low heat for 2 minutes.
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6
Put the sandwiches in the skillet, cover, and cook for 2 to 3 minutes, or until the undersides turn golden brown.
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7
Turn the sandwiches and, working quickly, separate 1 egg into a small cup, allowing the egg white to drip into the cup.
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8
Pour the yolk into the hole in the bread and then the egg white over it.
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9
Sprinkle with salt and pepper to taste.
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10
Repeat with remaining eggs and sandwiches.
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11
Cover and cook for 2 to 3 minutes, or until the undersides are golden brown, and the yolks have begun to set (the egg whites won't have cooked through yet).
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12
Carefully turn the sandwiches again (some of the egg white may run off).
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13
Cover and cook for 1 to 3 minutes, depending on how you like your eggs.
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14
Cut the sandwiches in half diagonally and serve immediately.
