In a mixing bowl, add flour and ground sea salt; whisk to combine. Transfer the flour mixture to the bowl of a food processor and form a well in the center.
In another bowl, beat the eggs before pouring in ½ cup of milk; whisk until well blended. Add the egg mixture to the well and, using the paddle attachment, process for 1 minute on low speed. Increase to speed 4 and process for 5 minutes, stopping halfway through to clean the sides of the bowl.
When time is up, add a little bit of milk, ½ a tablespoon at a time, and process for 30 seconds between each addition until the batter is smooth but not too runny. When the desired consistency is reached, let it rest for 10 minutes.
Add 1 tablespoons coarse sea salt to a large pot of water and bring to a boil. Working in batches, scoop batter into a spätzle press and push it through into the water. Cook the noodles for 2 to 3 minutes or until they rise to the top which is an indication they’re done.
Scoop them up into a bowl and transfer to a colander. Rinse the noodles immediately with cold water to stop the cooking process and drain them well; set aside while cooking the remaining batter.
In a skillet over medium-high heat, add butter and when it starts sizzling, add the cooked noodles. Sauté for about 4 to 6 minutes or until the edges start to brown a little bit. If desired, add seasoning and herbs like paprika, freshly ground black pepper, garlic powder, chives, dill, cheese, etc.
When the noodles start to change to a nice golden color, remove from the heat, sprinkle some fresh chopped parsley and serve immediately.