01 - Melt butter in a large pot over medium heat. Add diced onion, carrots, and celery. Sauté for 5 minutes until vegetables begin to soften and become fragrant.
02 - Stir in minced garlic and cook for 1 minute until fragrant, being careful not to burn it.
03 - Add cauliflower florets and diced potatoes to the pot. Cook for 2 minutes, stirring frequently to lightly coat with butter and aromatics.
04 - Pour in vegetable broth, then add dried thyme, smoked paprika, salt, and black pepper. Bring to a gentle boil, then reduce heat to low, cover, and simmer for 15 minutes until all vegetables are tender when pierced with a fork.
05 - Use an immersion blender to partially puree the soup, leaving some chunks for texture. Alternatively, carefully transfer half the soup to a countertop blender, blend until smooth, then return to the pot.
06 - Stir in whole milk and heavy cream. Bring to a gentle simmer over medium-low heat, stirring occasionally to prevent scorching.
07 - Gradually add shredded sharp cheddar cheese, a handful at a time, stirring constantly until fully melted and the soup is smooth and creamy. Taste and adjust salt and pepper as needed.
08 - Ladle hot chowder into bowls and garnish with freshly chopped chives and additional shredded cheddar cheese if desired. Serve immediately.