Step 1

Arrange a rack in the middle of the oven and heat the oven to 350°F. Place 1/2 cup walnuts on a baking sheet and toast in the oven until deeply golden and fragrant, about 8 minutes, shaking the pan halfway through. Meanwhile, cut 1 medium lemon into quarters. Reserve 1 piece for another use. Use your fingers to remove the seeds from the remaining 3 pieces as best you can. Transfer to a food processor fitted with the blade attachment and pulse until finely chopped but not puréed.

Step 2

When the walnuts are ready, set aside to cool slightly. Transfer to the food processor and add 1/4 cup grated Pecorino Romano cheese, 1 small garlic clove, 1/2 teaspoon granulated sugar, 1/4 teaspoon kosher salt, and a pinch red pepper flakes. Pulse a few times until the walnuts are finely chopped but not pasty.

Step 3

While pulsing, slowly pour 1/4 cup extra-virgin olive oil through the feed tube and pulse to combine; over-processing will make the olive oil bitter, so use a light hand here. You want the olive oil to be just incorporated and the pesto to still have some texture. Taste and season with more salt as needed.