How to Make It
In a saucepan, heat the olive oil. Add the peppers, garlic, onion and a pinch of salt. Cover and cook over moderately low heat until the peppers are softened, 8 minutes. Stir in the tomato paste, water and broth and bring to a boil. Cover and simmer over low heat until the peppers are very tender, about 10 minutes.
Transfer the soup to a blender and puree. Season with salt and pepper and refrigerate for about 1 hour, until lightly chilled.
Meanwhile, in a large skillet, heat inch of vegetable oil until shimmering. Add the tortilla strips and fry over moderately high heat until crisp. Drain and dust with the cheese. Serve with the chilled soup in shot glasses.