In a bowl, combine eggs, flour and milk. Mix to combine until it resembles pancake batter consistency. Set aside.
Set a pot of water to boil. Prepare an ice bath.
Add some olive oil to a skillet on high heat. Add the sliced scallions; when they begin to turn brown remove them and set aside.
Melt butter in a medium skillet. Once melted, add an equal amount of flour. Stir over medium-low heat. Add milk little by little while whisking until the consistency is similar to thin crepe batter. Add the grated cheese and stir until melted. Stir in the chopped scallions.
Pour the egg mixture into a colander. Holding it over the boiling water, start pressing with a rubber spatula, forcing the batter through the colander's holes. Once all batter has been pushed through, scoop the tiny pieces from the boiling water and place them in the ice bath.
Combine the chilled spaetzle with the cheese sauce; stir to warm through.
Transfer to a plate. Drizzle with balsamic vinegar and olive oil, and garnish with a sprinkle of paprika.