In a large saucepan, heat hot oil over medium heat. Add onion; cook until tender, stirring frequently. Add squash pulp, broth, and the water. Cook over medium-high heat until mixture just reaches boiling, stirring frequently. Stir in brown sugar, salt, the 1/4 teaspoon cinnamon, and the pepper. Remove from heat; cool slightly. Place half of the squash mixture in a blender or food processor. Cover and blend or process until smooth. Pour pureed squash into a medium bowl. Repeat with remaining squash mixture. Return all squash mixture to saucepan. Stir in half-and-half; heat through. If desired, garnish individual servings with pumpkin seeds and sprinkle with additional cinnamon.