1 cup finely shredded Gruyère cheese, plus 5 square slices Gruyère cheese
1 teaspoon kosher salt
1 teaspoon freshly ground black pepper
2 tablespoon chopped chives, for serving
Preheat the oven to 400°F.
In a small skillet, melt 1 to 2 tablespoons of the butter over medium heat. Add the panko and cook, stirring often, until lightly brown, 3 to 4 minutes. Transfer the panko to a small bowl and stir in the parsley. Set aside.
In a small skillet, melt 3 tablespoons of the butter over medium heat. Add the garlic and shallots and cook, stirring often, until softened, 2 to 3 minutes.
In a 9 x 13-inch baking dish, toss the Brussels sprouts with the shallot mixture until evenly coated. Spread the mixture in an even layer. Bake, stirring halfway through, until the sprouts are just tender, 25 to 35 minutes.
Meanwhile, make the cheese sauce. In a small microwave-safe dish, warm the milk for 1 minute.
In a small saucepan, melt the remaining 1 tablespoon butter over medium heat. Add the flour and cook, whisking constantly, 30 seconds. Slowly whisk in the warm milk and then the heavy cream. Bring to a simmer over low heat, whisking often, until thickened, about 4 minutes. Remove from the heat and begin adding the shredded Gruyère, stirring until melted, about 1 minute. Season with the salt and pepper.
Remove the Brussels sprouts mixture from the oven. Stir the cheese sauce into the mixture.
Arrange the sliced Gruyère on top of the Brussels sprouts mixture. Sprinkle with the panko. Return the baking dish to the oven and bake until the cheese is bubbly around the edges of the dish, 5 to 7 minutes. Garnish with the chives.
Store leftovers in an airtight container in the refrigerator for up to 3 days.