01 - In a large pot, melt the butter over medium heat. Add the chopped onion, diced celery, and diced carrots. Sauté for 5–6 minutes until the vegetables have softened.
02 - Stir in the minced garlic and cook for an additional minute until it becomes fragrant.
03 - Add the diced potatoes, broth, salt, pepper, paprika, and bay leaf to the pot. Bring the mixture to a boil, then reduce the heat to a simmer. Cook uncovered for 20–25 minutes, or until the potatoes are fork-tender.
04 - Carefully remove and discard the bay leaf. Use an immersion blender to partially blend the soup directly in the pot, or transfer approximately half of the soup to a standard blender, puree until desired consistency, and then return it to the pot. This technique leaves some potato chunks for texture.
05 - Stir in the whole milk and heavy cream. Simmer gently for 5 minutes, ensuring the soup does not come to a full boil after the dairy has been added.
06 - Remove the pot from the heat. Gradually stir in the grated Irish cheddar cheese until it is completely melted and the soup is smooth and creamy.
07 - Taste the soup and adjust the seasoning as needed with additional salt and pepper to achieve optimal flavor.
08 - Ladle the hot soup into individual bowls. Garnish generously with fresh chives and, if desired, crumbled cooked bacon before serving.