In a large mixing bowl, combine 2 cups of all-purpose flour and a pinch of salt. Create a well in the center and crack in 2 large eggs along with a tablespoon of olive oil. Using a fork, gradually incorporate the flour into the eggs until a shaggy dough forms. Knead the dough on a lightly floured surface for about 8-10 minutes until it's smooth and elastic.

Wrap the kneaded pasta dough in plastic wrap and let it rest at room temperature for at least 30 minutes.

After resting, divide the dough into four pieces. Using a pasta machine or rolling pin, flatten one piece of dough to about 1/16 inch thick. Cut the rolled dough into your desired pasta shape.

Bring a large pot of salted water to a boil. Add your freshly cut pasta and cook for 2-4 minutes, until it floats. Drain in a colander, reserving a cup of pasta water.

In a food processor, combine 2 cups of fresh basil, 1 roasted garlic clove, 1/4 cup of pine nuts, 1/2 cup of grated Parmesan cheese, and a squeeze of lemon juice. Pulse until finely chopped, then drizzle in 1/2 cup of olive oil while the processor runs until smooth.

In a skillet over low heat, combine the drained pasta and pesto sauce. Toss for 1-2 minutes, adding reserved pasta water if the sauce is too thick.

Serve immediately, garnishing with extra Parmesan cheese and fresh basil.