Process basil, cheese, pine nuts, and garlic in a food processor until finely chopped. Add 1 1/2 tablespoons oil; process until very finely chopped and fully combined, stopping to scrape sides of bowl as necessary. Set aside.
Heat remaining 1 1/2 teaspoons oil in a medium Dutch oven over medium. Add leeks; cook, stirring often, until softened, about 6 minutes. Stir in zucchini; cook, stirring occasionally, until zucchini is just tender but not browned, about 4 minutes. Add chicken stock, and increase heat to medium-high. Bring to a boil; reduce heat to medium-low, and simmer 8 minutes.
Meanwhile, cook tortellini in a stockpot of boiling water 3 minutes less than package directions, omitting salt and fat. Drain.
Add tortellini, spinach, and peas to soup. Cook until spinach is wilted, about 1 minute. Stir in lemon juice and salt. Ladle soup evenly into 4 bowls. Top each serving with pesto, and sprinkle evenly with pepper.