Add the pumpkin puree to the pot and stir well to combine with the onion and garlic. Slowly pour in the vegetable broth, stirring continuously until smooth.
Sprinkle in the ground cumin, smoked paprika, salt, and pepper. Mix well and bring the soup to a gentle simmer. Let it simmer for about 15-20 minutes to allow the flavors to meld.
Reduce the heat to low and stir in the heavy cream. Then, gradually add the shredded cheddar cheese, stirring constantly until melted and fully incorporated. Adjust seasoning as desired.
Ladle the creamy cheesy pumpkin soup into individual bowls. Garnish with fresh chopped chives on top for a pop of color and flavor.
Serve the soup warm with crusty bread on the side for dipping.