Into the bowl of a food processor, add All-Purpose Flour (2 cup), Salt (1/2 teaspoon), and Egg (1). Pulse for a few seconds.
Add Egg (2). Pulse until mixture forms pea-sized crumbs.
Add Olive Oil (3 tablespoon) while food processor is running. Mix until everything starts to pull together.
Turn mixture out onto a clean surface. Knead it a few times to bring it together.
Wrap dough in plastic wrap. Let sit for 1 hour.
Split dough into eight equal pieces. Working piece by piece, roll the first through a pasta machine on the widest setting.
Fold the outside edges into the center, making a square. Run through on the widest setting twice more.
Switch pasta machine to the next narrowest setting. Run through twice. Repeat this process until you reach the second to last narrowest setting.
Run each strip of dough through the pasta machine set to cut fettuccine.
Into a pot of boiling, salted water, add the noodles. Cook for 3-4 minutes. Drain, but save some of the pasta water.
Into a pan, add Butter (2 tablespoon). Once hot and bubbling, add Garlic (1 tablespoon) and enough pasta for one serving. Turn off heat and toss together.
Add Grated Parmesan Cheese (1/4 cup) and Ground Black Pepper (to taste). Stir to combine. Add a little bit of the pasta water to help coat the noodles evenly.
Plate pasta and garnish with Fresh Parsley (to taste).