Wash the broccoli and divide into small florets. Clean and peel the carrot, wash it and cut it diagonally into slices. Cook pasta in boiling salted water according to package instructions. Add vegetables for the last 5 minutes.
Pour off, rinse with cold water and drain. Roll up the ham and cut into slices. Whisk milk and egg, season with salt, pepper and nutmeg. Spread the pasta, vegetables and ham in a small casserole dish.
Pour egg milk over it. Bake in the preheated oven (electric cooker: 200 °C/ convection oven: 175 °C/ gas: level 3) for 25-30 minutes. Garnish with basil.