It's good to be kneaded! Working the dough develops its gluten, giving pasta that al dente texture you dig. Use plenty of flour when cutting your noodles to keep them from sticking.
Mound the flour on a work surface; season with a pinch of salt and make a deep well in the center. Crack the eggs into the well. Using a fork, scramble the eggs and gradually work the flour from the inner wall of the well into the eggs. Once the dough starts to come together, use your hands to work all the flour and egg together.
Scrape the dough into a ball. Using your hands or a stand mixer with the dough-hook attachment, knead the dough until smooth and firm, 8 to 10 minutes, adding a few drops of water if the dough is too dry. Form into a ball and wrap in plastic wrap; let rest at room temperature about 30 minutes.
Unwrap the dough and cut into 4 pieces; shape each into an oval about 1/3 inch thick. Working with 1 piece at a time, run the dough through a pasta roller, starting with the widest setting and gradually working down to roll through the thinnest, to create long, thin sheets.
Working on a floured surface, cut the sheets crosswise into 12-inch-long pieces, then cut each lengthwise into 3/4-inch-wide noodles. Transfer in small piles to a baking sheet and let rest until slightly dry but still pliable, about 30 minutes.