Pour 1 to 2 cups chicken broth in a blender; add onion, garlic, parsley, and thyme. Blend the onion mixture until liquefied; pour into a large stock pot.
Pour remaining broth into pot. Stir pumpkin puree into the broth; stir until smooth. Bring to a boil, reduce heat to low, and simmer, stirring occasionally, until beginning to thicken, about 45 minutes.
Remove pot from heat. Stir cream through the soup; season with salt and pepper.
