Preheat the oven to 400°F on the convection setting (if available). Rub 1 tablespoon of the butter on the bottom and sides of a 1 ½ to 2-quart casserole dish; set aside.

Boil the potatoes: Combine the potatoes, salt, and garlic clove in a large pot. Add enough cold water to cover the potatoes by a few inches. Bring to a boil over high heat. Reduce heat to medium-high and cook until the potatoes are very tender when pierced with a fork, 15 to 20 minutes. Drain in a colander set in the sink and leave the potatoes in the colander to steam-dry for 10 minutes.

Cook the green onions: While the potatoes are drying, add the remaining 5 tablespoons butter to the empty pot used to boil the potatoes and melt over medium heat. Add the green onions and cook until fragrant, 1 minute. Remove from the heat and set aside.

Mash the potatoes: Pass the potatoes and garlic clove through a potato ricer or food mill into the pot with the butter and green onions; discard the potato skins. Alternatively, pull the skins off of the potatoes with your fingers and mash the potatoes in the pot with a potato masher until smooth. Fold the potatoes into the butter mixture with a rubber spatula until evenly mixed.

Add the milk and assemble the casserole: Gently fold the milk into the potatoes in 3 additions. The mixture will be very loose but it will set up as it bakes. Add ½ teaspoon of the nutmeg and the cayenne pepper. Season to taste with salt and pepper. Spoon the potato mixture into the prepared casserole dish and sprinkle the cheese over the top.

Bake: Bake until the potatoes puff slightly and the cheese is melted and browned in places, about 30 minutes. If you oven does not have a convection setting, you can broil the casserole until browned on top after baking, 1 to 3 minutes. Sprinkle the remaining nutmeg over the top of the potatoes and serve immediately. Leftovers can be kept, covered, in the refrigerator for up to 5 days. Microwave until piping hot to reheat. Love the recipe? Leave us stars and a review below!