In a 10- to 12-inch frying pan over high heat, stir curry powder, turmeric, cumin, and cardamom seeds until fragrant, 20 to 30 seconds.
Add onion, bell pepper, ginger, and 1/2 cup broth; stir often until liquid has evaporated, 5 to 8 minutes. Add remaining 1 cup broth and the squash. Cover, reduce heat, and simmer until squash mashes easily, about 15 minutes. Uncover, return heat to high, and stir until liquid has evaporated, 4 to 8 minutes.
Remove from heat and mash mixture with a potato masher or coarsely puree in a food processor. Add salt to taste.