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 boil over high heat, then reduce to a simmer and cook for 15-18 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 deep golden and caramelized, about 15-20 minutes. Stir in the minced garlic during the last 2 minutes of cooking. Remove from heat and set aside.
04 - Return drained potatoes to the pot. Add butter, warm milk, sour cream, 1 cup of the cheddar cheese, all of the Parmesan, salt, and pepper. Mash until very smooth and creamy.
05 - Gently fold half of the caramelized onion mixture into the mashed potatoes. Taste and adjust seasoning with additional 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 evenly with the remaining 1/2 cup cheddar cheese.
07 - Bake uncovered for 20-25 minutes, 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.