In a large bowl, combine the flour and salt.
Make a well in the center. Add 4 of the eggs and the milk. Stir together with a wooden spoon to form a thick batter.
Bring a large pot of salted water to a boil. Decrease to a simmer over medium heat.
Place a spaetzle press or large holed colander over the pot and fill with batter.
Slide the press back and forth or use a wooden spoon to press the batter through the holes of the colander to create the dumplings.
Stir gently to remove any pieces from the bottom of the pot. Cook until they float to the top, remove with a strainer, and drain. Transfer to a large bowl.
Repeat with remaining batter.
In a medium bowl, beat together the remaining 4 eggs. Season with a pinch of salt and freshly ground black pepper.
Remove the lettuce leaves from the water.
In a large pan, drizzle the vegetable oil over medium heat. Add the cooked dumplings. Once heated through, pour in eggs. Stir continuously just until the eggs are barely set.
Serve immediately with the lettuce leaves.