Clean and cut all the "verdura" (including the bell peppers, tomatoes, zucchini blossoms, chili peppers) into 1/2-inch dice. Make sure to do the chili peppers last and clean your knife and cutting board thoroughly after chopping them.
In a 12 to 14-inch saucepan with 3-inch sides, heat the olive oil over a medium-high flame until hot but not smoking. Add the garlic and onion and cool until a light golden brown, about 5 minutes. Add the potato cubes and cook until light golden brown on all sides, about 5 minutes more. Add the rest of the vegetables and let cook until soft, about 15 minutes more.
Begin adding the stock, bit by bit. Bring the soup to a boil, reduce to a simmer, and season to taste with salt and pepper.
Serve the soup in 4 warmed soup bowls, garnished with basil. Add some Parmigiano-Reggiano, to taste, if desired.