Place the potato chunks in a large pot and cover with cold water by 2 inches. Stir in 1 tablespoon of kosher salt, cover, and bring to a boil over high heat.
Reduce the heat to medium-low and simmer until the potatoes are very tender and breaking apart, 15 to 20 minutes. Drain well and return the potatoes to the hot pot for 1 minute, shaking gently, to steam off excess moisture.
Add the softened cream cheese, butter, and garlic powder to the hot potatoes. Mash with a potato masher (or beat with a hand mixer on low) until smooth — but don't overmix, or the potatoes turn gummy.
Beat in the sour cream and warm milk until the potatoes are creamy and fluffy. Fold in 1 cup of the shredded cheddar, then season with salt and pepper to taste.
Butter a 9x13-inch casserole dish and spread the mashed potatoes in evenly, smoothing the top with a spatula.
MAKE AHEAD: Let cool completely, cover tightly with plastic wrap (press it right onto the surface), and refrigerate for up to 3 days.
On serving day, let the casserole sit at room temperature for 30 minutes. Preheat the oven to 375°F (190°C).
Sprinkle the remaining 1 cup of cheddar evenly over the top. Bake uncovered for 35 to 40 minutes (45 to 50 minutes if baking straight from the fridge), until the cheese is melted and golden and the edges are bubbling.
Let rest 10 minutes, shower with chopped chives, and serve warm.