To make the pasta dough: In an electric mixer fitted with a dough hook, combine the flour and salt. Add the eggs, 1 at a time, and continue to mix. Pour in 1 tablespoon olive oil and continue to mix until a smooth dough is formed. If the dough is too dry drizzle in a bit of water, if it is too wet sprinkle in some more flour. Dust some flour on a work surface, knead and fold the dough until it is elastic and smooth, this should take about 10 minutes. Brush the surface of the dough with the remaining olive oil and wrap the dough in plastic wrap; let rest for about 30 minutes to allow the gluten to relax.
To make the dough by hand: 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 olive oil to the well and lightly beat with a fork. Gradually draw in the flour from the inside wall and mix it with the beaten eggs. Use 1 hand for mixing and the other to protect the outer wall. Continue to incorporate all the flour until it forms a smooth dough. Dust some flour on the work surface; knead and fold the dough until it is elastic and smooth, this should take about 10 minutes. Brush the surface of the dough with the remaining olive oil and wrap the dough in plastic wrap; let rest for about 30 minutes to allow the gluten to relax.
To roll out the dough: Cut the ball of dough in half, cover and reserve the piece you are not using to prevent it from drying out. Dust the counter and dough with a little flour. Press the dough into a rectangle and roll it through a pasta machine set at the widest setting 2 or 3 times. Guide the dough with your hand as it emerges from the rollers to prevent it from puncturing or stretching. Dust the sheets with extra flour whenever the dough gets sticky. Reduce the setting and crank the dough through again 2 or 3 times. Continue reducing the setting and rolling until the machine is at its narrowest setting; the dough should be paper-thin, about 1/8-inch thick for ravioli. Roll out the other half.
Recipe courtesy of Tyler Florence