Wash the asparagus, cut off the woody ends. Cut the asparagus into pieces. Cook ribbon noodles in boiling salted water according to package instructions. Add the asparagus to the noodles about 5 minutes before the end of the cooking time.
Cut the ham into strips. Wash, clean and halve the tomatoes. Drain the pasta and let it drain. Whisk milk and eggs. Season with salt and nutmeg. Line an ovenproof dish with baking paper.
Mix the noodles with the ham, spread in the casserole dish. Pour egg milk over it and place tomatoes on the casserole. Cook in the preheated oven (electric cooker: 200 °C/ convection oven: 175 °C/ gas: level 3) for about 40 minutes.
After approx. 30 minutes, cover the casserole if necessary. Garnish with basil.