Peel and chop the Yukon Gold potatoes. Place them in a large pot, cover with cold salted water, and bring to a boil. Cook until fork-tender, about 15 minutes. Drain thoroughly.

Return hot potatoes to the pot or a large bowl. Add the butter, sour cream, warm milk, minced garlic, salt, and black pepper. Mash until smooth and fluffy.

Preheat oven to 375°F. Grease a 9×13-inch baking dish. Spread half of the mashed potatoes into the dish. Sprinkle with 1 cup shredded cheddar cheese. Add the remaining mashed potatoes and top with the final 1/2 cup cheese.

In a small bowl, mix the breadcrumbs with melted butter. Sprinkle over the top of the casserole.

Bake uncovered for 25–30 minutes or until the top is golden brown and bubbly. Garnish with chopped chives or green onions if desired.