Heat butter and oil in a large soup pan over medium-high heat.
Add onions and cook until very soft, about 5 minutes.
Mix in garlic and cook an additional minute, until fragrant.
Add broth, pumpkin, pumpkin pie spice, salt, cayenne pepper, and black pepper.
Bring pumpkin soup to a boil and lower to a simmer.
Simmer, covered, for 30 minutes. Stir occasionally.
Remove from heat.
Blend soup using an immersion blender or standing blender.
Mix in heavy cream and serve.