Halve and core the red peppers, spread them on a baking sheet, skin facing up. Halve the tomatoes and spread them on the baking sheet with the cut side up.
Drizzle with 1 teaspoon of olive oil, carefully sprinkle the sugar over it, then put a pinch of salt and a little black pepper on the vegetables and sprinkle with 1 tablespoon of the fresh basil.
Bake in the preheated oven at 190 ° C for 1 hour.
Heat the remaining olive oil in a large saucepan and carefully cook the onion and garlic in it for 15 minutes. Don`t get a tan !! Add the peppers and tomatoes to the onions and garlic in the saucepan. Then pour in the broth and bring everything to a boil. Cool a little and carefully puree with a hand blender. Sprinkle with the chopped basil when serving.