In a medium (4-quart) pot with a lid, heat 4 tablespoons of the olive oil over medium heat. Add the shallot, celery, the chopped jalapeno, and the garlic powder and cook, stirring frequently, until the vegetables have softened, about 5 minutes. Add 2 cups water and the cauliflower, chili powder, cumin, 1 teaspoon salt, and 1/4 teaspoon pepper. Bring to a boil, then reduce to a simmer. Cover and let simmer until the cauliflower is quite soft when pierced with the tip of a paring knife, about 30 minutes.

Meanwhile, heat the remaining 1 tablespoon olive oil in a medium skillet over medium-high heat. Add the chorizo and cook, stirring continuously to break apart the meat as it browns, until well cooked, crispy, brown, and crumbly, about 10 minutes.

Working in batches, puree cauliflower and cooking liquid in a blender until smooth, adding the heavy cream as you do; to prevent splattering, fill the blender only halfway. If the soup is too thick, add a little water. Transfer pureed soup to a clean pot, then whisk in the grated cheese in 5 additions, incorporating well after each. Season to taste with salt and pepper.