In a covered saucepan, heat the stock, cubed pumpkin, onion, garlic, salt, thyme, and peppercorns to boiling; reduce heat and simmer, uncovered, 20 minutes.
Remove 1/2 cup of the pumpkin with a slotted spoon; reserve.
Simmer remaining pumpkin mixture, uncovered, 20 minutes longer; transfer to a large bowl.
Preheat oven to 350F degrees.
Cut the top off the sugar pumpkin and remove the seeds.
Place the pumpkin on a baking sheet and bake for 20 minutes; set aside in a warm spot.
Puree 2 cups of the pumpkin mixture in a blender or food processor; return pureed mixture to the pot.
Repeat with remaining pumpkin mixture.
Heat pureed mixture to boiling; reduce heat; simmer, uncovered, for 10 minutes.
Stir warm cream and reserved pumpkin into soup.
Place the warmed sugar pumpkin on a platter; ladle the soup in and garnish with parsley.