Mound 3 1/2 cups flour in center of a large work surface, and make a well in the middle. Crack eggs into the well and add olive oil.
Using a fork, beat eggs; slowly incorporate flour, beginning with inner rim of well. When flour is incorporated, gather dough together to form a rounded mass. Begin kneading dough with the palms of your hands. Once dough comes together, scrape up any dried bits of dough; discard.
Lightly flour work surface; knead dough until smooth and elastic, about 6 minutes. Wrap dough in plastic wrap; let rest for 30 minutes at room temperature before using. Roll or shape as desired.