Melt butter in a Dutch oven over medium-high heat. Add onion to pot and cook, stirring, until soft, about 5 minutes.
Add ginger, cinnamon, and red-pepper flakes and stir. Add applesauce, pumpkin, broth, maple syrup, and salt. Stir to combine; then simmer 15 minutes.
Stir in half-and-half or cream; then purée in a blender (work in batches) until smooth.