In a large pot over medium-high heat, saute onion, garlic, and carrot in olive oil until just beginning to brown. Add chicken broth and bring to a boil. Add sweet potatoes and apples, cover, reduce heat to medium and let soup simmer until sweet potatoes and apples are very tender, about 15 minutes.
Once tender, transfer soup to a high-speed blender (depending on the side of your blender, you may have to do it in batches) Puree soup on high speed until completely smooth.
Return soup to pot and stir in thyme, parsley, and salt and pepper to taste. Bring soup to a low simmer over medium heat, then stir in warmed cream. Keep soup warm until ready to serve.
Ladle hot soup into serving bowls and garnish with parsley and shredded Asiago cheese if desired. Enjoy!