Preheat oven to 350°. Cut squash in half lengthwise with large heavy knife (use a hammer or flat mallet to help drive the blade through). Scoop out seeds.
Mix butter and curry powder and brush over cut surfaces of squash and onion. Put squash and onion, cut sides down, on a rimmed baking pan. Bake until soft when pressed, about 1 hour.
Scoop flesh out of squash and remove skin from onion. Chop onion. Purée squash and onion, in batches and holding lid down with a towel, with 3 cups broth and any juices from baking pan. Pour into a large pot and thin with more broth if you like. Add salt and cayenne, and cook, stirring, over medium-high heat until hot.
Divide among serving bowls and top each bowl with about 1 tbsp. yogurt.