Heat the olive oil in a large pot over medium heat. Add the sliced chorizo and cook until the edges brown and some fat renders out, about 5 minutes. Remove the chorizo with a slotted spoon and set it aside.
Add the diced onion to the same pot and cook in the rendered fat until it softens, about 4 minutes. Stir in the minced garlic and cumin and cook for 1 minute more.
Add the cauliflower florets and chicken broth. Season with salt and black pepper. Bring the mixture to a simmer and cook until the cauliflower is tender, about 15 minutes.
Use an immersion blender to partially puree the soup, leaving some chunks of cauliflower for texture. Return the cooked chorizo to the pot and stir to combine.
Ladle the soup into bowls and top each serving with the chopped cilantro.