Place the flour and black pepper in a food processor, pulse to combine. Add the eggs, water, and olive oil; pulse until dough resembles breadcrumb and all the flour is incorporated.
Transfer dough to a clean board and knead using the palms of both hands until the dough is smooth and forms a ball. Wrap dough in plastic wrap and let rest for 20 minutes.
Divide the dough into four wedges and process through pasta machine several times until thin and smooth.
Use the linguine cutter and run the dough sheets though cutter.
Bring a large pot of salted water to boil over medium-high heat. Carefully drop fresh pasta into boiling water and stir gently to keep from clumping. Cook for 2 – 4 minutes.