Place the cubed potatoes into a large pot and cover with cold water by about 1 inch. Season generously with salt, bring to a rolling boil over medium-high heat, and simmer until completely tender when pierced with a fork.

Preheat your oven to 191 °C (190 C) and lightly grease an 8x8-inch or 2-quart baking dish with butter.

Drain the cooked potatoes thoroughly in a colander, then return them to the warm dry pot over very low heat for 1 minute to cook off excess moisture.

Mash the potatoes using a potato masher or ricer until smooth. Fold in softened butter, warm heavy cream, warm milk, minced garlic, kosher salt, black pepper, and nutmeg until fully incorporated.

Stir half of the shredded Gruyere cheese directly into the warm mashed potatoes until melted, then spread the mixture evenly into the prepared baking dish.

Scatter the remaining Gruyere and grated Parmesan evenly across the top surface.

Bake in the preheated oven for 20 minutes until heated through and bubbling around the edges. Switch the oven to broil on high for 2 to 3 minutes until the cheese crust is deeply golden brown and blistered.

Remove from the oven, let rest for 5 minutes, garnish with freshly chopped chives, and serve warm.