Step 1

In a large pot over medium, heat the oil until shimmering. Stir in the onion, garlic and ½ teaspoon salt, then cover and cook, stirring occasionally, until the onion is softened but not browned, 6 to 8 minutes. Stir in the paprika and the cauliflower, then add the broth and 1 cup water. Bring to a simmer, then cover and cook until the cauliflower is fully tender, 15 to 20 minutes. Cool, uncovered, for about 5 minutes.

Step 2

Using a blender and working in 2 or 3 batches to avoid overfilling the jar, puree the mixture with the cheddar until smooth. Return the soup to the pot and heat over low, stirring, until heated through; do not simmer. Taste and season with salt and pepper. Serve drizzled with oil and sprinkled with pepper.