Place cauliflower pieces, carrot slices, potato pieces into a large bowl. Drizzle olive oil over veggies. Sprinkle minced garlic, paprika, turmeric, salt and pepper over veggies. Gently toss veggies with oil and spice mix all together. Spread veggies in an even layer over a rimmed baking sheet. Bake at 425 degrees for 20 minutes.
Allow roasted veggies to cool at room temperature slightly and then add to a large stockpot. Pour coconut milk and vegetable stock (or broth) over veggies. Puree with an immersion blender until smooth - or puree in a regular blender.