Take the cream cheese out of the fridge at least an hour prior to starting the recipe, or microwave it for 20-30 seconds (should be very soft). Preheat the oven to 375F and move the rack to the top third of the oven.
Melt the butter in a skillet over medium-high heat. Add the garlic and cook for about 30 seconds.
Stir in the cream cheese (I cut it into smaller pieces first), cream, and broth. Cook it for 4-5 minutes, stirring nearly constantly, until the cream cheese has melted in. Don't cook it for much longer because we don't want the sauce to get too thick since it still has to be baked.
Add the gnocchi and chicken to the skillet. Continue cooking, stirring often, for 3 minutes.
Stir in half the parmesan then remove the skillet from the heat.
Transfer the skillet mixture to a 9x13 baking dish. Spread it out in an even layer.
Top the gnocchi with the remaining parmesan and the mozzarella.
Bake, uncovered, for 25-30 minutes. Let it sit for 5 minutes prior to serving (the sauce will thicken a bit more as it cools). Season with salt & pepper if needed.
