Slice the onions into 1/4-inch-thick rounds and lay them in a shallow baking pan, such as a sheet pan or jelly roll pan. Drizzle with the olive oil and season to taste with salt and pepper. Roast for 15 to 18 minutes, or until lightly browned.
Meanwhile, in a medium saucepan, bring the cream and wine to a simmer over medium-high heat. As soon as the liquid starts to bubble around the edges, remove from the heat.
Spoon about 1-2 tablespoon of the cream mixture over each onion slice. Cover with aluminum foil, return to the oven, and cook for about 25 minutes. increase the oven temperature to 450°F.
Remove the foil and top the onions with the shaved cheese. Return the pan to the oven and cook for 4 to 5 minutes, or until the edges caramelize. Serve hot.