Preheat oven to 425 degrees, spray a rimmed baking sheet with cooking spray, and chop cauliflower, potato, and onion into roughly the same size pieces. Arrange vegetables and garlic cloves on the prepared baking sheet, toss with olive oil and smoked paprika to coat, and roast for 30 minutes (stirring halfway through).
Add roasted veggies to your food processor in batches and process them until they're at your desired soup consistency. (I pureed half and left half slightly chunkier for texture as shown above, but you can puree everything if you prefer a smoother soup.) Add the processed roasted veggies, corn, vegetable broth, sea salt, pepper, and cayenne to a large pot or Dutch oven, stir, and bring to a boil.
Reduce heat to medium-low and stir in milk and cheddar cheese, then simmer for about ten minutes to blend flavors. Taste and add a little more salt if necessary, and serve roasted cauliflower corn chowder topped with chopped green onions and additional cheddar (optional).
Notes
Roasted Cauliflower, Potato, and Corn Chowder is naturally gluten free; the potatoes thicken it up nicely with no need for the added flour you'll find in many cauliflower soup recipes.