Toast walnuts in a skillet for 3–4 mins until fragrant
Let walnuts cool and prepare basil
Boil salted water and cook pasta to al dente
Add walnuts and garlic to processor, pulse
Add basil, salt, pepper, and pulse again
Drizzle in olive oil while blending
Add cheese and lemon juice, pulse to combine
Toss cooked pasta with pesto and pasta water
Adjust seasoning with lemon juice or salt