Gather the ingredients. Preheat the oven to 475 degrees F (245 degrees C).

Place potatoes into a pot, cover with fresh, cold water by 2 inches, and add 2 tablespoons kosher salt. Set heat to high and bring to a boil. Reduce heat to medium and simmer until tender, testing by poking potatoes with a knife. The time will depend on the size of your potatoes but could be between 15 and 20 minutes.

Remove from the heat and let drain in a colander for 5 to 10 minutes.

Transfer into a large bowl and mash thoroughly with a potato masher until no lumps remain. Add butter, kosher salt, and Gruyere cheese. Mix and mash until everything has been incorporated.

Add cayenne, 3/4 cup Parmigiano-Reggiano cheese, and buttermilk, and mash until well combined. Taste and adjust for salt.

Whisk cream in a metal bowl until thick and fairly stiff peaks form, 1 to 2 minutes. Pour 1/2 of the whipped cream onto the potatoes and cut it in with the side of a spatula to lighten the mixture. Repeat with remaining whipped cream but do it carefully to preserve the maximum amount of volume, cutting in until just barely mixed.

Transfer into a well-buttered 2- to 2 1/2-quart casserole dish and distribute gently with a fork. Smooth the top with a spoon if desired. Sprinkle remaining 1/4 cup Parmigiano-Reggiano on top and dust lightly with cayenne.

Place the baking dish on a pan and bake in the center of the preheated oven until beautifully browned, 15 to 20 minutes.

Remove from the oven and sprinkle with green onions before serving.