In an electric mixer fitted with a dough hook, combine flour and salt. Add eggs 1 at a time and continue to mix. Drizzle in oil and continue to incorporate all the flour until it forms a ball. Sprinkle some flour on work surface, knead the dough until elastic and smooth. Wrap the dough in plastic wrap and let it rest for about 30 minutes to allow the gluten to relax.
Cut the ball of dough in half, cover and reserve the dough you are not immediately using to prevent it from drying out. Dust the counter and dough with flour. Form the dough into a rectangle and roll it through the pasta machine, 2 or 3 times, at its widest setting. Guide 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 until the machine is at its narrowest setting. The dough should be paper-thin, about 1/8-inch thick.
Mix all the ingredients until well combined and set aside.
Basil Cream Sauce:
Put the cream in a saucepan over medium heat until simmering.
Add in the mozzarella and cook until fully incorporated in the cream.
Add in the Parmesan and the basil.
Cook for 2 minutes until it begins to thicken.
Salt and pepper to taste.
Serve and enjoy!