Preheat the oven to broil on high (about 500°F). Slice the croissants in half and place them cut-side up on a sheet pan. Broil for 1–2 minutes until lightly golden and crisp, watching closely to prevent burning. Remove immediately.

Heat 3 tablespoons oil in a non-stick skillet over high heat until shimmering. Crack in the eggs and gently break the yolks. Reduce heat to medium-low, season with pepper, and cook 2–3 minutes. Flip and cook another 1–2 minutes until fully set and no longer runny (internal temperature 160°F). If eggs spread too much, cook in batches or use egg rings.

Warm ham in the skillet for 30–45 seconds per side, or cook bacon over medium heat for 6–8 minutes until crisp. Drain on paper towels.

Layer ham (or bacon), one egg, and one slice of American cheese on each croissant bottom. Add the tops.

Microwave each sandwich for 15 seconds to melt the cheese, adding 5–10 seconds if needed. Or warm in a 350°F oven for 5 minutes until the cheese softens.