Peel the potatoes and cut them into small, even cubes.
Melt the butter in a large pot over medium heat. Add the onion and garlic, then sauté until the onion is soft and translucent.
Add the diced potatoes and stir to coat them with the butter and aromatics.
Pour in the chicken or vegetable broth. Bring to a gentle boil, then reduce the heat and simmer until the potatoes are fork-tender, about 15–20 minutes.
Blend the soup with an immersion blender until smooth. Alternatively, carefully blend it in batches in a countertop blender and return it to the pot.
Stir in the heavy cream and simmer gently for 3–5 minutes. Do not let the soup boil vigorously.
Season with salt and black pepper to taste.
Ladle into bowls and garnish with chives, grated cheese, bacon bits, or your preferred toppings.