For the broccoli casserole with tomato sauce, blend broccoli, eggs, QimiQ, nutmeg, salt and pepper in a blender until smooth. Butter four ramekins or coffee cups and sprinkle with breadcrumbs. Pour in the broccoli mixture and cook in the preheated oven, in a bain-marie, for about 25 minutes at 180°C.
For the sauce, sauté the shallots in oil until translucent, add sugar and balsamic vinegar and cook for 2 minutes, add diced tomatoes and basil, season with salt and pepper and cook for another 10 minutes on low heat. Remove the casserole dish from the oven, carefully remove the broccoli casserole from the dish and serve with the tomato sauce.