Whisk flour, milk, egg, crème fraîche, salt, and cayenne pepper together in a bowl until batter drips slowly off whisk. Add a bit more flour if batter seems too thin; add a bit more milk if batter seems too thick.

Bring a large pot of salted water to a simmer over medium-high heat. Push a spoonful of batter into the simmering water through the smooth side of a cheese grater with fairly large holes using a spatula.

Cook spätzle in batches until they rise to water’s surface, about 3 minutes. Remove spätzle with a slotted spoon. Repeat with remaining batter.