Preheat your oven to 375°F. In a large pot, bring water to a vigorous boil and season generously with kosher salt. Meanwhile, prepare a large bowl filled with ice water. Add the Brussels sprouts to the boiling water and blanch for about 2 minutes, just until their color turns vibrant green. Immediately transfer them to the ice bath to halt the cooking process. Let them chill for around 5 minutes, then drain thoroughly and arrange evenly in a 13" x 9" baking dish.

In a large skillet over medium-low heat, melt the butter until it begins to bubble slightly. Add the chopped shallots, garlic, thyme, and black pepper. Cook, stirring occasionally, for about 4 minutes or until the shallots soften and become fragrant.

Reduce the heat slightly and stir in the heavy cream, sour cream, a pinch of nutmeg, and about 2 teaspoons of kosher salt. Allow the mixture to gently warm through, then remove the skillet from heat. Add the grated Parmesan and half of the shredded mozzarella cheese, stirring continuously until the cheeses melt completely into a smooth, velvety sauce.

Pour the creamy cheese sauce over the blanched Brussels sprouts in the baking dish, tossing gently to ensure everything is well coated. Sprinkle the remaining 1/2 cup of mozzarella over the top to form a golden, bubbling crust as it bakes.

Place the dish uncovered in the oven and bake for 25 to 30 minutes, or until the mixture is bubbly and the top is golden brown. Remove from the oven and garnish with fresh chives just before serving.

Make Ahead Tip: You can assemble the entire dish up to two days in advance. Cover tightly with plastic wrap and store in the refrigerator. When ready to serve, uncover and bake as directed for a hassle-free, flavorful side.