Preheat broiler. Rub the bell pepper and poblano chile with 1 tablespoon olive oil. Place them under the broiler skin side up and cook until the skins are blistered and black. Remove from the broiler, and when cool enough to touch, peel and discard skins. Thinly slice the pepper and chile, and set aside.
Crack the eggs into a bowl. Add basil, season with salt & pepper, and beat lightly with a fork.
In a large nonstick skillet with an ovenproof handle, heat 2 tablespoons olive oil over high heat, spreading the oil around to coat the bottom and sides of the pan. Add the sliced pepper, potatoes, chile, stirring and cook until the potatoes are tender, then add the mushrooms, spinach, and garlic, and cook for about 1 minutes, stirring.
Pour in the egg mixture and scramble gently with a wooden spoon for about 30 seconds or until the mixture forms small curls. Then leave to cook undisturbed for another 45 seconds or until the frittata is just set.
Remove the skillet from the heat and place it under the broiler for 30-40 seconds or until the frittata firms up and lightly browns. Be careful not to overcook the frittata or it will become tough and dry.
Lay out the prosciutto on a large warm serving plate. Remove the pan from the broiler and slide the frittata onto the plate on top of the proscuitto. Sprinkle generously with Parmigiano-Reggiano.
To serve, cut the frittata into wedges.
You can really use any combination of vegetables for a frittata, whatever you have on hand, and top with whatever cheese you like.