Mix flour and salt in a medium bowl and make a well in the center. Lightly beat eggs with oil. Pour the egg mixture into the center of the flour. Use your hands to begin to incorporate the eggs into the flour, working the flour in from the sides a little at a time, until it begins to hold together. (Add a few drops of water if the pasta is too dry to hold together, or a little more flour if it is too sticky.) Knead the dough on a well-floured surface, using the heels of your palms. It will take about 15–20 minutes to work the dough until it is smooth and elastic.
Divide the dough into 6 pieces and shape into flat balls. Cover with a damp towel, and let rest for about 20 minutes.
Use your hand to flatten a ball of dough on a floured surface into an oblong shape, about 1" thick. Dust the top with flour. Use a rolling pin to roll out the dough, turning it several times and dusting with flour, until it is paper thin. Repeat until all your dough is rolled out.