Adding water to the skillet helps cook the eggs evenly without burning the bagel halves, resulting in a lightly toasted bagel wrapped around a perfectly runny yolk. Savory smoked salmon and creamy avocado complete this classic breakfast.
If needed, carefully widen holes in bagel halves to 1 3/4 inches in diameter using a paring knife. Spread bagel halves evenly on both sides with butter. Heat a 12-inch skillet over medium. Place bagel halves, cut sides up, in skillet. Cook until golden brown, 2 to 3 minutes.
Flip bagel halves cut sides down. Reduce heat to low; crack eggs into bagel holes. Pour 1 tablespoon water around edge of skillet, and immediately cover skillet. Cook until egg whites are set and yolks are cooked to desired degree of doneness, 5 to 8 minutes. Transfer bagel halves to a plate; season with salt and pepper. Serve with smoked salmon and caviar or sliced avocado.