01 - Preheat oven to 375°F. Lightly grease a 9x13-inch baking dish with butter or nonstick spray.
02 - Place peeled and chunked potatoes in a large pot and cover with cold, salted water. Bring to a rolling boil, then reduce heat and simmer for 15 to 18 minutes until fork-tender. Drain thoroughly.
03 - While the potatoes cook, heat olive oil in a large skillet over medium heat. Add the thinly sliced onions and sauté, stirring frequently, until deeply golden and caramelized, about 15 to 20 minutes. Stir in the minced garlic during the final 2 minutes of cooking.
04 - Return drained potatoes to the pot. Add butter, warm milk, sour cream, 1 cup of the cheddar cheese, Parmesan, salt, and pepper. Mash until completely smooth and creamy.
05 - Gently fold half of the caramelized onions into the mashed potato mixture. Taste and adjust salt and pepper as needed.
06 - Spread the potato mixture evenly into the prepared baking dish. Scatter the remaining caramelized onions over the top, then sprinkle with the remaining 1/2 cup of cheddar cheese.
07 - Bake uncovered for 20 to 25 minutes, or until the cheese is fully melted, bubbling, and lightly golden on top.
08 - Remove from the oven and let rest for 5 minutes. Garnish with fresh chives if desired, then serve warm.