Preheat the air fryer to 325°F (163°C) for 3-5 minutes.
Lay bread flat and press a flat-bottomed glass firmly into the center of each slice to create a well about 2.5-3 inches wide and 1/4 inch deep without pressing through the bread.
Spread softened butter evenly across the top surface of each bread slice, focusing on the outer edges and rim around the well.
Crack each egg into a small bowl first, then gently tip it into the center of the well on the bread. Season immediately with salt and pepper.
Carefully place the prepared bread slices in the air fryer basket in a single layer with space between slices. If using parchment liners, place them in the basket first.
Air fry at 325-350°F (163-177°C) for 7-8 minutes for a runny yolk with set whites, 9 minutes for a semi-firm jammy yolk, or 10-11 minutes for a fully firm yolk.
If adding shredded cheese, open the air fryer at the 6-minute mark and sprinkle it over the egg, then continue cooking.
Carefully slide a wide spatula under each slice to remove, transfer to a plate, and garnish with chives, smoked paprika, or everything bagel seasoning. Serve immediately.