In a large Dutch oven, melt butter over medium heat. Add onion, garlic, and thyme; cook for 5 minutes. Stir in potatoes and popped corn; cook for
1 minute, stirring constantly. Add broth; bring to a boil. Cover, reduce heat, and simmer for 30 minutes, stirring occasionally. Remove thyme sprigs.
Spoon half of soup into the container of a blender. Secure lid on blender, and remove center piece of lid to let steam escape; place a clean towel over opening in lid to avoid splatters. Process soup until smooth. Repeat procedure with remaining soup; return all soup to pot.
Stir in corn, and cook until heated through, about 10 minutes. Gradually stir in cheese until melted. Top servings with Truffled Popcorn Topping. Garnish with thyme, if desired.