Preheat the oven to 400°F (200°C). Generously grease a 12-cup muffin tin with cooking spray and set aside.
Press 1 slice of deli ham into each muffin cup, gently shaping it into a little “cup.” Trim the slices if they are very large or hanging far over the edges.
Sprinkle about 1 tablespoon of shredded cheddar cheese into the bottom of each ham cup.
Carefully crack 1 egg into each muffin cup on top of the cheese, trying to keep the yolk intact if you can.
Season the tops of the eggs lightly with kosher salt and freshly ground black pepper.
Bake for 12 to 15 minutes, until the whites are set. Bake closer to 12 minutes for a softer, runnier yolk and closer to 15 minutes for a more firm yolk.
Remove the pan from the oven and let the ham and egg cups cool for a minute. Run a spoon around the edges of each cup and gently lift them out of the muffin tin.
Sprinkle with chopped fresh parsley if using and serve warm.