In a large pot over medium heat, cook the onion and carrots in olive oil until softened, about 3 minutes.
Pour in the chicken broth, roasted garlic, and seasonings. Bring to a low boil for 10 minutes with the lid on to let the flavors meld.
When it's safe to handle, carefully blend until smooth and creamy, or leave just a few chunks. I like to use my immersion blender but you can also use a regular blender. If it's really hot, don't fully seal the lid.
Separately in a bowl or glass, mix the cream and flour together.
Add the chicken to the soup, then slowly stir in the heavy cream and flour mixture, finally adding the cheddar cheese until melted and silky. Taste and adjust the salt as needed.