Melt butter in a pot over medium-low heat. Add onions and a large pinch of salt. Cook and stir until onions have softened but not taken on any color, about 10 or 15 minutes.

Cut off ends of squash. Carefully cut squash in half lengthwise and remove the seeds. Peel the squash with a vegetable peeler. Cut into chunks.

Raise heat under the pot to medium-high. Stir in tomato paste; cook and stir until mixture begins to caramelize and turn brown, about 2 minutes. Add squash, chicken broth, 1 teaspoon salt, and cayenne pepper. Bring to a simmer; reduce heat to medium-low and simmer until squash is very tender, 15 to 25 minutes. Reduce heat to low. Blend with an immersion blender until very smooth. Stir in cream and maple syrup; add more salt if needed.