Preheat the oven to 475°. In a large skillet, heat 1/2 tablespoon of the vegetable oil. Add the smoked ham and cook over moderately high heat until browned on the bottom, about 2 minutes. Using a slotted spoon, transfer the ham to a plate. Add 1 1/2 tablespoons of the vegetable oil to the skillet along with the garlic, onions, Scotch bonnet chiles and green bell pepper. Cover and cook over moderately low heat, stirring occasionally, until the vegetables are softened, about 12 minutes. Stir in the paprika and cook over moderately high heat for 1 minute. Add the tomatoes and cook until they release their juices, about 2 minutes. Stir in the ham and season the sofrito with salt and pepper.
Meanwhile, wrap the tortillas in aluminum foil and warm them in the oven. In a large cast-iron skillet, heat 1/2 tablespoon of the vegetable oil. Crack 4 of the eggs into the skillet, season with salt and pepper and fry sunny-side up over moderate heat, until the egg whites are set and the egg yolks are still slightly runny, about 3 minutes. Transfer the eggs, yolk side up, to a plate and keep them warm by tenting them with aluminum foil. Add the remaining 1/2 tablespoon of vegetable oil to the skillet and fry the remaining eggs.
Set 2 tortillas on each plate. Top with the fried eggs, spoon the sofrito on the side and serve.
Notes: Variations: Use the sofrito in cheese quesadillas or on grilled chicken, or toss with roasted new potatoes.