Gather the ingredients. Fill a stockpot with water and bring to a boil. While the water is coming to a boil prepare the pesto.
The Pesto
Briefly soak and wash the 2 cups basil leaves in cold water, and gently pat it thoroughly dry with paper towels.
Add the 45 g pine nuts to a dry skillet over medium low heat. Cook the pine nuts until fragrant and golden brown, about 5 minutes, stirring occasionally so that the pine nuts don't burn. Remove from heat and set aside.
In a food processor with the blade attachment add the baked 45 g pine nuts, 2 cups basil leaves, 1 Tbps. lemon juice, 3 cloves garlic, 1/2 Tbps. salt and 1/2 Tbps. black pepper. Pulse until well combined and scrape down the sides of the food processor if needed. Drizzle in the 1/2 cup extra virgin olive oil and process until fully combined and set aside in a mixing bowl.
Mix in the grated 40 g Parmigiano Reggiano cheese and 30 g Pecorino Romano cheese by hand. Combine the cheese with the previous pesto mix the add the softened 40 g unsalted butter, distributing it uniformly into the sauce.
Once the water has come to a boil add the 450 g tagliatelle pasta and cook per package instructions. Reserve 1 cup reserved pasta water and drain the pasta.
Return the pasta to the stockpot. Stir in the pesto and 1 cup reserved pasta water until the sauce fully coats the pasta. Add in more pasta water if needed to get the desired consistency of your pesto sauce. Serve as desired.