Fill a large pot with water, add oil, and bring to a boil.
Place flour in a large mixing bowl and make a well in the middle.
Add salt, eggs, and water and beat the dough until smooth and bubbly. The dough should have a thick consistency. Fill a spaetzle press with the dough and squeeze into the boiling water (You may use a colander to push the dough through or a wooden cutting board and scrape dough little by little with a knife into the water).
When the spaetzle float to the top of the pot, drain them.
Place half of the spaetzle in a glass baking dish and add a layer of sauerkraut on top.
Add another layer of spaetzle and sauerkraut. Cover the pan to keep the dish warm.
In a separate pan melt the butter and add breadcrumbs just long enough to moisten them. Top the spaetzle with the breadcrumbs.
Serve all layers together, or reheat the next day in a little bit of butter.