With just two ingredients, this pasta dough comes together easily. You will need a pasta roller to create the thin sheets. Save your scraps as you layer the lasagna—you may need them to fill in gaps as you work.
Mound flour on a large wooden cutting board or in a large mixing bowl. Make a well in the center, and add eggs. Beat flour and eggs with a fork, starting with the inner rim of the well, to incorporate. As you incorporate the eggs, keep pushing the flour up to retain the well shape (don't worry if it looks messy). Dough will come together once half the flour is incorporated.
Knead dough using both hands, primarily using your palms. Add more flour if dough is very sticky. Once dough is formed, lift it from the board and scrape up any leftover dry bits. Lightly flour board, and continue kneading dough for 3 minutes more. (Dough should be elastic and slightly sticky.)
Continue kneading dough for 3 minutes more, dusting board with flour if needed. (Dough should be smooth and elastic.) Wrap dough in plastic wrap, and let stand at room temperature for 20 minutes.
Divide dough into 8 pieces. Flatten each using your palm or a rolling pin, and flour both sides of each piece; cover dough with a kitchen towel. Pass 1 piece of dough through the rollers of a pasta machine set on the widest setting, using one hand to guide it and prevent it from folding or rippling. Fold sheet of dough neatly into thirds, then pass it through the rollers again.
Continue passing dough through widest setting, sprinkling flour on both sides of dough each time to prevent it from sticking to itself, until it is silky and smooth. Pass dough through next widest setting twice, flouring both sides of dough each time. Repeat, reducing each setting, and running dough through twice on each until you reach the thinnest setting, and transfer to a baking sheet. Cut out two 8-by-21-inch sheets and twelve 13-inch-long sheets.
Bring a large pot of salted water to a boil. Cook 2 or 3 sheets at a time, plus any scraps, for 1 minute. Drain, and transfer to a wire rack, and let drain for a few minutes. Pat sheets dry with paper towels.