Cook linguine al dente, following the directions on the package.
Before draining, carefully scoop out ⅓ cup of pasta cooking water with a measuring cup and set it aside.
Drain the pasta.
While the pasta is cooking, coarsely chop the garlic.
In a food processor or blender, combine olive oil, garlic, and basil.
Process until you have a moist, well-mixed paste.
Transfer the paste to a small bowl and stir in Parmesan cheese, salt, pepper, and the reserved pasta cooking water.
This is your pesto.
In a large serving bowl, combine the pesto and linguine, toss well, and serve.