In a large pot, combine the diced potatoes and chicken or vegetable broth; bring the mixture to a boil, then reduce heat and simmer until the potatoes are tender, which should take about 10-15 minutes.

While the potatoes are cooking, melt butter in a separate saucepan over medium heat, then add the chopped onion and cook until softened, about 3-5 minutes.

Stir in the minced garlic and cook for another minute until fragrant, then whisk in the flour and cook for about 1 minute to create a roux.

Gradually whisk in the milk until smooth and thickened, then add the heavy cream and heat through without boiling.

Once the potatoes are tender, mash some of them directly in the pot to thicken the soup, leaving some chunks for texture.

Pour the cream mixture into the pot with the potatoes, stirring to combine, then season with salt and pepper to taste.

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