Rinse the tomatoes, remove the stalk approaches and cut the flesh into cubes. Peel the cucumber. Rinse the peppers, cut in half and remove seeds and ribs. Dice cucumber and peppers. Mix 100 grams (approximately 1/2 cup) diced tomatoes, 100 grams (approximately 1/2 cup) diced cucumber and half the diced peppers and set aside. Puree the remaining diced vegetables in a blender along with 25 ml (approximately 1/8 cup) of olive oil. Season with salt, pepper and chile pepper. Chill until ready to serve.
Rinse the basil, shake dry and cut into strips. Heat the remaining olive oil (25 ml, approximately 1/8 cup) in a pan and cook the diced vegetables that were set aside for 5 minutes, stirring occasionally. Season with salt and pepper, then let cool to room temperature.
Serve the puréed soup in soup plates and top with the cooked vegetables. Garnish with basil leaves.