Dump the flour in a pile on a work surface. Make a deep, wide well in the center and pour in the eggs, olive oil, and salt. Begin mixing the eggs with a fork, staying in the center and being careful that the eggs don’t breach the wall. Little by little, mix in flour from the sides until the dough starts to move as a unit and is too stiff to mix with a fork. Continue mixing by hand, incorporating more flour to stiffen the dough. When it doesn’t easily absorb more flour (one signal is floury, dried bits of dough flaking off the mass), set the dough aside; scrape up all the remaining flour and pass it through a sieve to sift out any dried-up bits. Discard the bits and keep the cup or two of sifted flour on the work surface to use during kneading if necessary.
A deep, wide well of flour makes a tidy mixing bowl.
Wash and dry your hands. Knead the dough on the lightly floured surface until it’s a smooth, homogenous ball of dough, firm but resilient, neither too dry nor too soft, about 5 minutes; it should no longer stick to the surface. Poke it and it should spring right back; press your finger into the center and it should feel just a bit tacky. If it’s very sticky, knead in more flour.
When the dough is sufficiently kneaded, a finger dent will bounce back.
Wrap the dough loosely in plastic and refrigerate for at least 1 hour, or up to 8 hours.