Red Pesto Fettuccine

Name: Red Pesto Fettuccine
Ingredients: 1 lb. fettuccine (or other long, thin pasta such as spaghetti or linguine); 1/2 cup raw walnuts; 3 medium cloves garlic, smashed; 3 Tbsp. extra-virgin olive oil; 1/2 cup drained julienned sun-dried tomatoes in oil plus 2 Tbsp. oil from jar (from a 5-oz. jar); 2 Tbsp. tomato paste; 2 oz. Parmesan cheese, grated (about 3/4 cup), plus more for topping; 1 Tbsp. fresh lemon juice (from 1 lemon); 1/4 tsp. crushed red pepper, plus more to taste; 1/2 tsp. kosher salt, plus more for cooking pasta