Preheat the oven to 400ºF.
Form spaetzle dough by combining the flour, eggs, salt, nutmeg, and about 3/8 cup water in a bowl. Vigorously stir until bubbles form. Allow the dough to sit for 15 minutes.
In a big pot bring salt water to a boil. Using a spaetzle board and scraper, place the spaetzle dough onto the board and slowly scrape off into the water. It takes about 2-3 minutes for the spaetzle to cook. Remove them from the water and rinse with cold water to stop them from cooking further. Set aside in an oven-safe dish.
Peel and shred the carrots. Slice the tomatoes into halves. Chop the onion. In a skillet melt the butter. Add the carrots, pepper pieces, peas, and onion, and lightly cook for about 3 minutes. Flavor with salt and pepper.
Add the vegetables to the spaetzle and stir. Sprinkle with cheese and place the dish in the oven for about 5 minutes or until the cheese has melted.