Preheat your oven to 400°F and grease a 9x13-inch baking dish with butter.
Bring a large pot of salted water to a boil and blanch the Brussels sprouts for 4-5 minutes until just tender, then drain well.
In a medium saucepan, combine heavy cream, milk, garlic, thyme, nutmeg, salt, and pepper, heating over medium until it just begins to simmer.
Remove from heat and stir in 1 cup of Gruyere and all the Parmesan cheese until melted and smooth.
Arrange the blanched Brussels sprouts in the prepared baking dish, cut side up.
Pour the cheese sauce evenly over the Brussels sprouts, making sure they're well coated.
In a small bowl, mix together panko breadcrumbs, melted butter, and remaining 1/2 cup Gruyere cheese.
Sprinkle the breadcrumb mixture evenly over the top of the gratin.
Bake for 25-30 minutes until the top is golden brown and bubbly, then let rest for 5 minutes before serving.