In a large saucepan or Dutch oven, heat the oil over medium-high heat. Add the onion and cook, stirring occasionally, until softened, about 5 minutes.
Combine the cornstarch with 3 tablespoons vegetable broth, stir until smooth, and set aside.
Add the rest of the broth and the queso to the pot and bring to a simmer. Add the broccoli and carrots, reduce heat, and simmer for 10 minutes or until the vegetables are tender. Add the cornstarch mixture and cook for 1-2 minutes, until the soup is thickened.