Preheat the oven to 350 degrees F (180 degrees C) with racks in center and upper third (about 3 inches from heat source) positions. Grease a 7x11-inch baking dish with butter.

Heat 2 tablespoons butter in a large pot over medium heat until melted and foaming. Add flour; cook, whisking constantly, for 1 minute. Slowly whisk in cream until smooth. Whisk in rosemary, salt, black pepper, onion powder, and garlic powder. Heat over medium, whisking often, until cream is steaming; remove from heat. Whisk in 1/2 cup of the Gruyère and 1/4 cup of the Parmigiano-Reggiano until smooth.

Stir potatoes into cream mixture, breaking up slices until potatoes are evenly coated in cream mixture.

Stack about 3 inches of potato slices neatly in your hand, then lay them in the prepared baking dish, standing up vertically. Continue to stack and place potatoes in baking dish, moving around the perimeter and filling the center, until all the slices are added. Pour remaining cream mixture evenly over potatoes. Cover dish tightly with aluminum foil.

Bake in the preheated oven on the center rack until potatoes are almost tender, about 1 hour and 30 minutes. Remove foil and continue baking until browned on top, 20 to 25 minutes.

Remove potatoes from the oven, and increase oven temperature to Broil. Sprinkle evenly with remaining 1/2 cup Gruyère and 1/4 cup Parmigiano-Reggiano. Broil on upper rack until cheese is melted and lightly browned, 2 to 3 minutes. Let cool for 15 minutes. Garnish with rosemary before serving.

Serve and enjoy.