In a saucepan over medium heat, melt the butter. Add the minced garlic and sauté until fragrant, about 1 minute.
Pour in the heavy cream and bring to a gentle simmer. Stir in the Parmesan cheese, Italian seasoning, salt, and pepper, allowing it to thicken for 3-4 minutes.
Add the shredded chicken to the sauce, coating it well, then remove from heat.
Cut the tops off the sourdough bread loaves and scoop out some of the insides to create bowls, leaving about a half-inch border.
Lightly brush the inside of the bread bowls with some melted butter and sprinkle with a pinch of garlic powder (if desired).
Spoon the Chicken Alfredo mixture into each bread bowl until filled to the top.
Sprinkle the mozzarella cheese evenly over the filled bowls.
Place the bread bowls on a baking sheet and bake for 15-20 minutes, or until the cheese is bubbly and golden brown.
Remove from the oven and let cool for a few minutes before garnishing with freshly chopped parsley. Serve warm.