Combine ⅓ cup pine nuts and 2 tablespoons oil in a large Dutch oven; cook over medium heat, stirring often, until the pine nuts are toasted and brown, 5 to 6 minutes. Using a slotted spoon, transfer the toasted pine nuts to a small bowl, reserving the oil in the pot.
Add chopped shallots, chopped garlic, ½ teaspoon salt and ½ teaspoon pepper to the reserved oil in the Dutch oven. Cook over medium-low heat, stirring often, until softened, about 2 minutes. Stir in 12 ounces pasta and 4 cups water; bring to a boil over high heat, stirring occasionally. Reduce to a lively simmer; cover and cook, stirring occasionally, until the pasta is almost al dente, about 6 minutes (some liquid will remain).
Stir 10 ounces frozen peas into the pasta mixture; cook, uncovered, over medium-low heat, stirring often, until the peas are heated through and the pasta is al dente, about 2 minutes. Remove from heat; stir in ⅔ cup basil, ¼ cup Parmesan, 3 tablespoons pesto, 1 teaspoon lemon zest and 2 tablespoons lemon juice. Divide among 6 bowls and sprinkle with the reserved toasted pine nuts. Garnish with additional Parmesan, if desired.
