Heat oil in a Dutch oven over medium heat. Add onion and leeks; cook, stirring occasionally, until translucent and tender, 3 to 5 minutes. Add garlic; cook, stirring often, until fragrant, about 1 minute. Stir in basil, salt and pepper.
Add broth and Parmesan rind. Cover and bring to a boil over medium-high heat; reduce heat to medium-low to maintain a simmer. Add tortellini; cover and cook until al dente, about 4 minutes. Add asparagus and peas; cook, uncovered and stirring occasionally, until the vegetables are bright green and tender, 2 to 3 minutes. Remove and discard the Parmesan rind.
Divide the soup among 6 bowls. Top each with 2 teaspoons Parmesan and serve with a lemon wedge.
