Preheat oven to 375°. Fill a large pot with water, sprinkle in some salt and bring to a bowl
While the water in heating, rinse the Brussels sprouts, trim off the ends and cut them in half lengthwise. Prepare an ice bath by filling a large bowl with ice & cold water
Add the Brussels sprouts to the boiling water until the leaves turn bright green, about 3-4 minutes. Drain sprouts, then immediately transfer to ice water. Allow them to chill for ~5 minutes to stop the cooking process. Drain well, then transfer to a 9" x 6" baking dish
Combine the half-and-half, Greek yogurt, nutmeg and salt in a medium bowl then whisk together until well-combined and smooth.
In a large skillet, melt the butter over medium heat. Add the green onions, garlic, rosemary, and pepper, stirring occasionally for about 3 minutes. Slowly stir the half-and-half/yogurt mixture to the pan with the onions and garlic until evenly combined, then remove from heat. Make sure you don’t over-heat the cream sauce or it will become too thick.
Add the Parmesan & 1/2 cup of the mozzarella cheese. Continue stirring just until melted & smooth then pour the cream mixture over Brussels sprouts
Toss gently to coat, then sprinkle the remaining 1/2 cup mozzarella over the top of the spouts and transfer to the oven. Bake uncovered for 30 minutes or until the cheese is bubbly & golden brown
Remove from the oven and serve