Clean and wash the broccoli and cut it into florets. Cook the pasta in a large pot in boiling salted water for about 10 minutes. Cook broccoli for 3-4 minutes, add frozen peas for 2 minutes. Drain noodles together with vegetables, rinse and drain.
Cut ham slices into small squares. Wash and halve the cherry tomatoes. Grate cheese roughly. Separate eggs. Whisk egg yolk and milk. Season with pepper and nutmeg, stir in half the cheese.
Beat the egg white and 1 teaspoon salt until stiff and fold into the egg milk.
Mix the pasta-vegetable mixture, ham and tomatoes in an ovenproof dish spread with a little oil. Pour the egg milk over it and sprinkle with the rest of the cheese. Bake in the preheated oven (electric cooker: 200 °C/circulating air: 175 °C/gas: level 3) for approx. 40 minutes.
Peel and finely chop the onion. Heat 1 tablespoon of oil. Sauté onion in it. Sweat tomato paste briefly. Add the chopped tomatoes and bring to the boil. Season with salt, pepper and 1 pinch of sugar. Simmer at low heat for about 15 minutes.
Wash parsley, shake dry and chop. Stir into the tomato sauce, season to taste again. Arrange pasta casserole and tomato sauce.