Heat oil in a large pot over medium-high; add onion and cook, stirring occasionally, until brown and soft, about 10 minutes. Add peppercorns, garlic, and thyme. Cook, stirring often, until fragrant and slightly brown, about 2 minutes.

Stir in pumpkin puree; cook, stirring occasionally, until puree turns a few shades darker, about 5 minutes. Stir in stock, maple syrup, salt, nutmeg, and cinnamon. Simmer, uncovered, on medium-low heat, stirring occasionally, until slightly reduced, about 30 minutes.

Transfer soup to a blender in batches; secure lid (hold down with a kitchen towel), and blend until smooth, about 30 seconds per batch.

Return soup to the pot; stir in heavy cream. Cook over medium heat until heated through, about 4 minutes.

Ladle soup into bowls and garnish with fresh parsley.