Roast the poblanos: Add the poblano peppers to a baking sheet and place under the broiler for 10 minutes until the skin is blackened and blistered, flipping halfway through.
Remove them from the oven, loosely cover the baking sheet with aluminum foil or plastic wrap to keep in some of the heat and help them steam, and let them sit for 5 minutes.
Pull and rub off as much of the loose skin on the peppers as possible. It doesn't have to be perfect. (View some step-by-step photos on how to roast poblano peppers here.)
Transfer poblanos to a cutting board, discard the stem and discard the seeds and veins if you don't want them spicy. Cut poblanos into long strips and chop into bite-sized pieces.
Prepare oven and muffin tin: Preheat the oven to 350°F. Generously spray a 12-cup muffin tin with cooking spray or grease with olive oil.
Make the seasoning:Combine the black pepper, onion powder, garlic powder, and salt in a small bowl.
Assemble: Place 2 slices of deli ham into the bottom of each muffin cup and press down on the bottom and sides to form a little cup/boat. (If you're using 12 large slices of ham total, use 1 slice per muffin cup.)
Evenly distribute the chopped roasted poblanos into each muffin cup, then carefully crack an egg on top of each and sprinkle with the seasoning.
Bake for 20-25 minutes or until the eggs are cooked through, firm, and no longer jiggly.
Cool: Remove the muffin tin from the oven and let it cool for 10 minutes. Use a toothpick or knife to loosen the sides of each muffin cup and lift them out.
Notes
To store: Leftovers can be stored in an airtight container in the fridge for up to 5 days.
To reheat: Egg cups can be reheated in the microwave in 30-second increments until warmed through.
To freeze: Once cooled, place the baked eggs in a freezer-safe zip-top bag and freeze for up to 3 months.