Peel and dice the potatoes into 1-inch pieces. Chop the onion and mince the garlic.

In a large pot, melt butter over medium heat. Sauté the chopped onion until softened, about 3-4 minutes.

Add minced garlic and cook for another minute until fragrant. Stir in the flour and cook for 1 minute to create a roux.

Gradually whisk in the broth and milk until smooth, ensuring no lumps remain.

Add the diced potatoes, salt, and pepper. Bring the mixture to a boil, then reduce heat and simmer until potatoes are tender, about 10-15 minutes.

Using an immersion blender, carefully blend a portion of the soup to desired creaminess. Alternatively, mash some of the potatoes with a fork against the side of the pot.

Stir in the heavy cream and heat through for 2-3 minutes, but do not boil.

Ladle the hot soup into bowls and garnish with fresh chives before serving.