Bring warm salted water to the boil in a saucepan and cook the thin spaghetti (I had Capellini No. 1) in it for 3 minutes, drain and rinse with cold water.
In the meantime, whisk the egg with the milk, salt and pepper and mix in the grated cheese. Cut the cocktail tomatoes into small pieces, drain the mozzarella and cut into thick slices.
Melt the butter in an ovenproof pan (without plastic handle) on the stove and during this time mix the spaghetti with the egg and cheese mixture well. Pour into the pan and fry on medium heat for about 2-3 minutes. Don`t stir! The bottom should be lightly browned and you should be able to lift it up with a spatula. Then place the pan in the oven on medium setting and bake for about 8-10 minutes. Now distribute the mozzarella on the spaghetti and turn on the grill. Let it melt for 5 minutes. Can also be used without a grill, it may take 3 minutes longer.
Remove the pan, spread the tomatoes and a few leaves of basil on it. Possibly add a little salt.