To make pasta dough: Combine the flour and salt on a flat work surface; shape into a mound and make a well in the center. Add the eggs and 1 tablespoon of the olive oil to the well and lightly beat with a fork. Gradually draw in the flour from the inside wall of the well in a circular motion. Use 1 hand for mixing and the other to protect the outer wall. Continue to incorporate all the flour until it forms a ball. Knead and fold the dough until elastic and smooth, this should take about 10 minutes. Brush the surface with remaining olive oil and wrap the dough in plastic wrap; let it rest for about 30 minutes to allow the gluten to relax.
Cut the ball of dough in 1/2, cover and reserve the dough you are not immediately using to prevent it from drying out. Dust the counter and dough with a little flour. Form the dough into a rectangle and roll it through a pasta machine, 2 or 3 times, at widest setting. Pull and stretch the sheet of dough with the palm of your hand as it emerges from the rollers. Reduce the setting and crank the dough through again, 2 or 3 times. Continue tightening and rolling until the sheet is about 1/4-inch thick; (keep in mind, overly thick pasta tastes gummy.)
Now, using the spaghetti cutting attachment, run the sheets through the cutting slot. Dust the noodles and a baking sheet with cornmeal. Coil the spaghetti strands into a nest and allow the pasta to dry for about 10 minutes before boiling.
Bring a large pot of salted water to a boil and add spaghetti. Cook for a few minutes until al dente.