Place squash, cut side down, in a baking pan drizzled with 1 tablespoon oil. Bake for 35-40 minutes, until squash is tender. Carefully scoop out squash into a bowl and set aside.
In a saucepan heated with oil, sauté onion and chili for 3-5 minutes. Stir in cumin, turmeric, cardamom pods, squash, and broth and bring to a boil. Reduce heat and simmer, covered, for 20-25 minutes.
Remove the cardamom pods. Add cilantro and puree soup. Season with sea salt and pepper to taste. Garnish with cheese and pumpkin seeds, if desired.