Trim the leeks, halve and rinse under running water. Rinse the carrot and slice both the leek and carrot. Rinse the green beans and cut into bite-sized pieces. Cut the cauliflower and broccoli into florets and rinse. Blanch the tomatoes in hot water, peel, remove the seeds and dice. Halve, seed and chop the peppers.
Melt the butter in a large saucepan, add the vegetables and saute briefly. Deglaze with the broth and simmer over low heat about 30 minutes. Season with salt and pepper and stir in the basil. Drizzle the olive oil over the soup and serve sprinkled with Parmesan cheese.