Fill a large pot with lightly salted water and bring to a rolling boil. Stir in tortellini and cook uncovered, stirring occasionally, until tender yet firm to the bite, 10 to 11 minutes. Drain.
Melt butter in a large pot over medium heat. Add carrots and onion; cook and stir until slightly softened, about 5 minutes. Add chicken broth, tomatoes, dandelion greens, garlic powder, basil, salt, and black pepper. Bring to a boil. Reduce heat to medium-low and simmer until flavors combine, 10 to 15 minutes.