Peel the onions and slice into thin half rings. Fry in plenty of butter over medium heat for 8-15 minutes, stirring occasionally, until golden brown or as dark as you prefer.
Sift the flour into a bowl. Add the eggs, mineral water, and a pinch of salt. Mix by hand or with a mixer, beating until the dough becomes bubbly and smooth. Adjust the consistency with water or flour as needed. Let the dough rest.
Preheat the oven to 80°C (176°F) with a baking dish inside. Bring a large pot of salted water to a gentle simmer. Grate all the cheeses and combine them.
Working in batches, pour the dough into a spaetzle slicer and shave the spaetzle directly into the simmering water. Stir gently to prevent sticking to the pot bottom. Once the spaetzle floats to the surface, cook for about 30 seconds, then skim out with a slotted spoon. Transfer to the preheated baking dish and sprinkle with a layer of the mixed cheese. Repeat until all the dough is used.
Distribute the browned onions over the cheese spaetzle and serve with a green salad dressed with vinaigrette and a cold beer.