Preheat oven to 375°F (190°C). Cut off the top third of the loaf lengthwise, scoop out the interior leaving a 3/4-inch shell, and brush the inside with butter and a pinch of salt.

In a saucepan over medium heat, melt 2 tbsp butter and sauté the minced garlic for 30 seconds. Whisk in the heavy cream and cream cheese, stirring until smooth, about 2 minutes.

Stir in the Parmesan, salt, and pepper, then fold in the shredded chicken. Warm through 1 minute and remove from heat.

Place the hollowed loaf on a parchment-lined baking sheet. Sprinkle 1 cup mozzarella into the shell, spoon in all the chicken mixture, top with the remaining 1 cup mozzarella, and set the bread lid back on.

Bake for 15 minutes at 375°F until the cheese melts and the crust is golden. Let rest 5 minutes, then slice thickly and serve with a sprinkle of parsley.