Heat olive oil in a medium pot over medium heat. Add the diced onion and sauté until tender and translucent.
Add the tomatoes and cook until they begin to break down. Stir in the paprika, rosemary, and thyme. Cook for another minute until fragrant.
Add the pumpkin puree, roasted red peppers, water, and Better Than Bouillon. Stir to combine. Reduce the heat to medium-low and simmer for 10 minutes.
Turn off the heat and puree the soup with an immersion blender until smooth. Stir in the milk or half-and-half. Season with salt. Return the soup to low heat and simmer gently for another 5 minutes. Add more water if the soup is too thick.
Serve warm with freshly ground black pepper and additional rosemary leaves for garnish.