In a large pot, melt the butter over medium heat, then add the chopped onions. Cook until they're translucent, about 5 minutes, and then stir in the garlic for an additional minute until fragrant.

Sprinkle the flour over the sautéed vegetables in the pot. Stir constantly for about 2 minutes to cook out the raw flour taste.

Gradually whisk in the broth while adding the diced potatoes. Season with salt and pepper. Bring the mixture to a boil, then reduce the heat and let it simmer until the potatoes are tender, about 15-20 minutes.

Using an immersion blender, blend the soup to your desired consistency—chunky or smooth.

Stir in the milk or cream and allow it to simmer on low for an additional 5 minutes. Adjust seasoning as needed.

Ladle the soup into bowls and enhance it with your chosen toppings before serving.