Add about 2 tablespoons of the olive oil to a blender, followed by the garlic, toasted pine nuts, basil, and salt. Pulse several times on low until the basil is chopped and the mixture begins to come together.

With the blender running on its lowest speed, slowly drizzle in the remaining olive oil just until incorporated. Stop and scrape down the sides as needed. Do not overblend; the pesto should retain some texture.

Add the Pecorino Romano and Parmigiano-Reggiano. Pulse only a few times, just until combined.

Add the lemon juice and pulse once or twice. Taste and adjust with additional salt or lemon juice, if needed.