Fill a large pan with 1 inch of oil. Heat the oil over medium heat, until a tortilla crumb sizzles gently when it hits the oil. Add 1 tortilla at a time and fry until halfway crisp. Remove and let drain on a cooling rack. Repeat with the remaining tortillas.
Heat 1 tablespoon of oil and 1 tablespoon of the butter in a pan over medium heat. Add the plantain and sauté until golden, about 6 minutes. Reserve for plating.
In the same pan, heat another 1 tablespoon oil and the remaining 1 tablespoon butter over medium heat. Add the eggs and fry until you have soft yolks.
Assemble the motuleños: Place 2 tortillas on each plate, layer each tortilla with 1 slice of ham and 1 fried egg. Top each egg with habanero salsa, 4 or 5 slices of plantain, the peas, and queso fresco. Serve with black beans, if you like.