Melt the butter or warm the olive oil in a large pot over medium heat.
Add the onion and cook for 5 to 7 minutes, stirring occasionally, until softened.
Add the garlic and cook for about 30 seconds, or until fragrant.
Stir in the canned pumpkin or homemade pumpkin purée.
Add 2 ½ cups of broth, thyme or sage, and nutmeg.
Bring the soup to a gentle simmer.
Cook uncovered for about 10 minutes, stirring occasionally.
Remove the pot from the heat.
Blend with an immersion blender until smooth.
Stir in ½ cup of cream.
Return the soup to low heat and warm gently.
Season with salt and black pepper to taste.
Add the remaining broth or extra cream as needed to reach your preferred consistency.
Serve warm with roasted pumpkin seeds, croutons, parsley, black pepper, or a drizzle of cream.