In a medium sized mixing bowl, whisk together the flour and 1/2 teaspoon salt.
Ina large mixing bowl, whisk together the eggs and milk.
Whisk the flour mixture into the milk mixture to create a loose dough that more resembles a thick pancake batter. It shouldn't be super runny. The thinner the batter is, the smaller your noodle pieces will be. The thicker the batter is, the bigger the pieces will be.
Cover the bowl with plastic wrap and let the dough sit for 10 minutes
Put a large pot of water onto the stove over high heat to boil. Make sure you use a tall pot to give the noodles room to cook properly.
Once the water is boiling, salt the water with 1 teaspoon of salt.
Push the batter through large holes in a cheese grater or colander, about 1 cup at a time.
Let the noodles cook for 3 minutes, stirring occasionally.
Use a slotted spoon to remove the cooked noodles from the water and place them in a large bowl while you repeat with the remaining batter.
To serve, either toss the cooked noodles in the melted butter, or pan fry the noodles in the butter until slightly golden and crispy, 3 minutes per side.
Notes
Store leftover noodles in an airtight container in the fridge for up to 5 days. Reheat in the microwave, pan fry with some butter, or reheat in the air fryer until hot.