Wash and roughly chop the potatoes into even 1-inch chunks (peel or leave them unpeeled if you don’t mind the texture of skins). Try to make the chunks as even as possible.
Place the potatoes in a large pot and cover with 1 inch of cold water. Stir in 1 tablespoon kosher salt. Bring to a boil.
Once boiling, cook until they are very tender, about 10 to 15 minutes (pierce a piece of potato with a fork to assess doneness). Drain and allow to steam while sautéing the garlic in Step 4.
When the potatoes are done, melt the butter in the same pot. Add the minced garlic and sauté for 1 to 2 minutes, until fragrant but not browned. Remove the heat and pour in the milk, stir for 15 seconds to warm the milk. Then add the potatoes back to the pot.
Mash the potatoes with a masher. Add the sour cream, prepared horseradish, and 1 ¼ teaspoons kosher salt and mash more until a creamy texture forms. (Adjust the horseradish amount to taste; 2 tablespoons has just a hint of horseradish and 4 tablespoons has a more pronounced flavor.)
Optional: For the creamiest mashed potatoes, transfer to a stand mixer. Add the whisk attachment and whip on low speed for 1 to 2 minutes, until fluffy (take care not to over whip or the potatoes will become too thick and gluey).
Serve immediately garnished with chopped fresh chives, if desired. Leftovers store up to 4 days refrigerated (or make them into potato pancakes or potato waffles!).