Preheat your oven to 375°F. While it heats, grease a 9x13 inch baking dish thoroughly with the melted butter, making sure to coat the bottom and sides evenly—this prevents sticking and adds richness to the bottom layer. In a medium bowl, whisk together the room temperature eggs, heavy cream, vanilla extract, cinnamon, sugar, and nutmeg until the mixture is smooth and well combined. I like to use freshly ground cinnamon here because the flavor is noticeably brighter than pre-ground varieties.
Arrange the 12 frozen cinnamon rolls in the prepared baking dish in a single layer, spacing them evenly so they have room to expand as they bake. Pour the custard mixture from Step 1 evenly over the rolls, making sure the liquid seeps into all the gaps and around each roll. The rolls don't need to thaw first—the overnight soaking (or even a few hours) allows the custard to fully penetrate them, creating a wonderfully moist, custardy texture throughout.
Bake in the preheated 375°F oven for 30-35 minutes, until the custard is set but still slightly jiggly in the very center and the tops of the rolls are golden brown. Remove from the oven and let the casserole cool for about 10 minutes—this resting time allows the structure to set slightly, making it easier to serve without falling apart, and gives you time to prepare the frosting.
Spread or drizzle the cream cheese frosting generously over the warm casserole, allowing it to melt slightly into the nooks and crannies. I find that applying frosting while the casserole is still warm helps it distribute more evenly and creates a more luxurious texture. Serve immediately while still warm for the best flavor and texture.