Rinse squash and cut in half lengthwise (if necessary, use a mallet to gently pound knife through squash). Scoop out seeds and discard; with a small, sharp knife, pare peel and discard.
Cut squash into 1-inch chunks; you should have about 4 cups.
In a 3- to 4-quart nonstick pan over medium-high heat, stir onion and ginger in olive oil until onion is very limp, 8 to 10 minutes.
Add cumin and curry powder; stir until fragrant, about 30 seconds.
Add 1 3/4 cups broth and the squash; bring to a boil, then cover, reduce heat, and simmer until squash is tender when pierced, 18 to 20 minutes.
In a blender or food processor, holding down lid with a towel, whirl squash mixture, in batches, until smooth. If sauce is thicker than desired, whirl in a little more broth.