01 - In a large pot, melt the butter over medium heat. Add onion, celery, and carrots, and sauté until softened, about 5 minutes.
02 - Stir in garlic, thyme, and smoked paprika, and cook for 1 minute until fragrant.
03 - Add potatoes, corn, bay leaf, and vegetable broth. Bring to a boil, then reduce heat and simmer uncovered for 15–18 minutes, until potatoes are tender.
04 - Remove bay leaf. Using an immersion blender, puree about one-third of the soup directly in the pot for a thicker consistency, or transfer a few cups to a blender and return to pot.
05 - Stir in milk and cream. Gently heat through without boiling, about 2–3 minutes. Season with salt and pepper to taste.
06 - Ladle into bowls and garnish with chopped chives or parsley if desired. Serve hot.