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

While potatoes cook, melt butter in a separate skillet over medium heat, then sauté the chopped onion until softened, about 3-5 minutes.

Add minced garlic to the skillet and cook for one minute more until fragrant, then stir in the flour and cook for another minute to create a roux.

Gradually whisk the milk and heavy cream into the roux in the skillet, cooking until the mixture thickens, then pour this into the pot with the cooked potatoes and broth.

Season the soup with salt and pepper, stir well, and heat through; for a smoother soup, you can mash some of the potatoes in the pot or use an immersion blender.

Ladle the creamy potato soup into bowls, garnish with shredded cheddar cheese and fresh chives, and serve immediately.