Preheat the broiler*.
Bring a large pot of water to a boil. Salt generously, then add the tortellini and cook according to the package directions. Drain and reserve.
Meanwhile, in a large skillet, melt the butter over medium-high heat. Add the garlic and cook for 30-60 seconds. Whisk in the flour and cook for another minute. Add the milk, whisking, and cook until the mixture has thickened.
Grate in a bit of fresh nutmeg, then season with salt and pepper. Add the spinach, artichoke hearts, and cooked tortellini. Stir to mix.
Pour the mixture into a 9x13-inch casserole dish and sprinkle the cheeses on top. Broil until the cheeses are melted, 1-2 minutes. Serve.
