In a soup pot, heat the oil over medium-high. Add the chorizo and cook until browned, about 5 minutes. Add the onion, bell pepper, zucchini, jalapenos and garlic; season with salt and pepper. Partially cover and cook until the vegetables soften, about 10 minutes. Add the spices and stir 1 minute. Add 2 cups stock, the tomatoes, corn and beans. Reduce the heat and simmer uncovered until the chili thickens, 10 minutes; season.
Meanwhile, in a large saucepan, bring the remaining 2 cups stock and 1 cup water to a boil. Gradually whisk in the polenta. Cook, whisking often, until thick and creamy, 5 to 8 minutes. Stir in the cheese.
Divide the polenta among bowls and form a well in each. Top with the chili and scallions.