Lay out the bread on a work surface and use a glass or a rolling pin to flatten.
Place a circle of ham in the middle of 4 slices of bread. Top with one circle of cheddar and another slice of ham.
Place the remaining slices of bread on top and, using the lid of a mason jar or a cookie cutter, press down to create 4 pockets. Make sure the seams are closed, pinching to seal if necessary. Reserve the bread with the circle cut-outs.
Place the pockets on a baking sheet.
In a small bowl, mix the melted butter and garlic. Brush the pockets with garlic butter.
Bake for 15 minutes, or until toasted.
Place the reserved bread on a baking sheet and brush with the remaining garlic butter.
Crack 1 egg into each circle, and season with salt and pepper.
Bake for 5 minutes, or until the yolk is cooked to your preference.
Serve the egg bread with the ham and cheese pockets and sprinkle with chives.
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