Prepare the Vegetables: Start by peeling and dicing 4 medium potatoes, 1 medium onion, 2 stalks of celery, and 2 medium carrots. Next, mince 2 cloves of garlic. Accurate prep is essential for uniform cooking and flavor.
Sauté the Aromatics: In a large pot, melt 3 tablespoons of unsalted butter over medium heat. Add the diced onions, celery, and carrots. Sauté the mixture until the vegetables start to soften, which should take about 5 minutes. Add the minced garlic and cook for an additional minute until fragrant.
Cook the Potatoes: Pour in 4 cups of chicken or vegetable broth and bring the mixture to a boil. Once boiling, add the diced potatoes. Reduce the heat and let it simmer for about 15 minutes, or until the potatoes are tender.
Thicken the Soup: In a separate pan, create a roux by melting another tablespoon of butter. Sprinkle in 2 tablespoons of all-purpose flour and whisk constantly for about 2 minutes until it turns golden brown. Gradually whisk in 1 cup of whole milk or half-and-half until the mixture thickens, about 3-5 minutes. Stir the roux into the simmering pot.
Blend and Finish: Using an immersion blender or a standard blender, puree the soup to your desired consistency, whether you prefer it creamy or with some chunky bits. Stir in ½ cup of heavy cream and adjust seasoning with ½ teaspoon of salt and ¼ teaspoon of black pepper. For added flavor, consider tossing in ¼ teaspoon of smoked paprika.
Serve: Ladle the steaming soup into bowls and top with your favorite toppings such as crispy turkey bacon, shredded cheddar cheese, or a dollop of sour cream.