Place the flour on a clean work surface and make a nest. Add the eggs, olive oil, and salt to the center and use a fork to gently break up the eggs, keeping the flour walls intact as best as you can. Use your hands to gently bring the flour inward to incorporate. Continue working the dough with your hands to bring it together into a shaggy ball.
Knead the dough for 8 to 10 minutes. At the beginning, the dough should feel pretty dry, but stick with it! It might not feel like it's going to come together, but after 8-10 minutes of kneading, it should become cohesive and smooth. If the dough still seems too dry, sprinkle your fingers with a tiny bit of water to incorporate. If it's too wet, add more flour onto your work surface. Shape into a ball, wrap in plastic wrap, and let rest at room temperature for 30 minutes.