Step 1

To prepare the caramelized onions, place a large skillet over medium heat, add the oil. Add the sliced onions to the skillet and cook the onions until they turn caramel in color, about 10-15 minutes.

Step 2

Cut potatoes into equal pieces and place in a stockpot. Cover potatoes with water and place the pot over medium heat. Bring the water to a boil. Cook potatoes for 8-10 minutes or until the potatoes are fork-tender. Drain. Return potatoes to the pot and add the butter and the half and half. Mash potatoes with a potato masher until smooth.

Step 3

Add 1/2 cup of the grated cheese to the potatoes and stir until incorporated. Add rosemary and half of the onions.

Step 4

Place potatoes in an ovenproof baking dish and top with the remaining onions. Sprinkle the remaining 1/4 cup of cheese over the onions and place under the broiler until the cheese has melted.