Cook bulgur according to package instructions.
Heat extra-virgin olive oil in a large frying pan over medium heat. Add onion and cook, stirring occasionally, until translucent but not browned, 6 to 7 minutes. Add carrots and cook until slightly softened, 3 to 4 minutes. Stir in broth, chickpeas, corn, bell peppers, salt, and pepper and bring to a boil. Boil 2 minutes to reduce by about a third.
Reduce heat, add zucchini and yellow squash, and simmer, stirring occasionally, until zucchini and squash are tender but not mushy, about 10 minutes. Add lemon juice and 1/4 cup basil.
Divide bulgur among 4 bowls, top with vegetables, sprinkle with remaining 1/4 cup basil, and drizzle with olive oil.