In a large skillet, sauté the peppers, onions, and, if using, the tomatoes in the olive oil over a moderate flame for about 5 minutes, then add a drizzle of water, lower the heat and cover the skillet partially. Let the vegetables braise until they are perfectly tender, adding more water if things begin to dry out. Take care to avoid any browning. Season the vegetables generously with salt and pepper while they cook.
Transfer the vegetables to a blender or food processor, along with a couple of basil leaves if you have them on hand. Start to blend/process them adding cream in a steady stream until you have a smooth and pourable, but still rather thick, purée. Taste and adjust for seasoning.
Transfer the purée back into the skillet and keep at a very slight simmer, adding pasta water if things get too dry.
Cook the pasta in well salted water until just a bit under the al dente stage.
Transfer the pasta to the skillet with the purée, along with a ladleful of the pasta water. Toss the pasta with the purée over a gentle flame until the purée has thickened enough to coat the pasta well. Add grated cheese and toss once more to let the cheese melt into the sauce.
Serve immediately, with additional grated cheese for those who want it.