Step 1: Cook the potatoes

1. In a large pot, combine the diced potatoes, chopped onion, garlic, and chicken or vegetable broth.
2. Bring to a boil over medium-high heat, then reduce the heat to medium-low. Simmer for 15-20 minutes, or until the potatoes are tender and easily pierced with a fork.

Step 2: Make the roux

1. In a small saucepan, melt the butter over medium heat. Stir in the flour and cook for 1-2 minutes, whisking constantly, to form a roux.
2. Gradually whisk in the milk, continuing to stir until the mixture thickens slightly. Remove from heat.

Step 3: Blend and thicken the soup

1. Use a potato masher to partially mash the cooked potatoes in the pot, leaving some chunks for texture. For a smoother soup, blend a portion of the mixture using an immersion blender or standard blender.
2. Stir the roux into the soup, mixing well. Add salt, pepper, and smoked paprika (if using). Cook for another 5-10 minutes, stirring occasionally, until the soup thickens to your desired consistency.

Step 4: Serve

1. Ladle the soup into bowls and garnish with your favorite toppings, such as bacon, cheese, green onions, or sour cream. Serve warm with crusty bread or crackers.