Halve the bagels and butter the cut sides.

Enlarge the holes in the center of each bagel half to about 1 inch in diameter.

In a heavy fry pan over medium-high heat, place the bagel halves buttered side down in batches.

Cook for approximately 2 minutes, or until golden brown on the bottom.

Transfer all bagel halves, cut side down, to a rimmed baking sheet.

Carefully break an egg into the center of each bagel half.

Sprinkle each egg with equal amounts of salt and pepper.

Evenly distribute the shredded cheddar cheese over the eggs.

Bake in a preheated 400F oven for 8 to 10 minutes, or until the eggs are set but the yolks are still soft.