Heat the butter in a 4-quart saucepan over medium-high heat. Add the onion and cook until the onion is tender-crisp.
Stir the broth, brown sugar, thyme, black pepper and pumpkin in the saucepan and heat to a boil. Reduce the heat to low. Cover and cook for 10 minutes or until the pumpkin is tender.
Stir the apples in the saucepan. Cook for 5 minutes or until the apples are tender. Mash the pumpkin mixture, adding additional broth, if needed, until desired consistency.