Grease your 9×13-inch dish generously with the melted butter, making sure to coat the corners. This step keeps the edges from sticking and helps them crisp up nicely as they bake. A well-buttered dish also makes cleanup much easier later.
Open your cans of cinnamon rolls and cut each one into quarters using a sharp knife or scissors. Scatter the pieces evenly across the baking dish so no spot is overly crowded. Set the icing packets aside for later; you'll need them at the very end.
In a large bowl, whisk together the eggs, heavy cream, milk, vanilla, cinnamon, and nutmeg until fully combined. The mixture should look pale and slightly frothy with no visible streaks of egg white. This custard is what turns plain dough pieces into something soft and bread-pudding-like.
Pour the custard evenly over the cinnamon roll pieces, gently pressing down any dry spots so they soak up the liquid. Drizzle the maple syrup over the top for extra flavor. Let it sit for a few minutes so the dough can absorb some of the mixture before baking.
Bake in a preheated 350°F oven for 30 to 35 minutes, or until the top is golden brown and the center is set. Cover loosely with foil if the top starts browning too quickly. You'll know it's ready when a toothpick inserted in the center comes out mostly clean.
While the casserole is still warm, microwave the icing packets (mixed with cream cheese if using) for about 20 seconds until pourable. Drizzle generously over the top of the baked casserole. Serve it warm, while the icing is still soft and glossy.