Preheat the oven to 375°F. Using a serrated knife, cut a circle into the top of each bread loaf and hollow out the interior, leaving about ¾ inch of bread lining the walls and bottom.
Melt 4 tablespoons butter with 2 minced garlic cloves. Brush generously inside each hollowed bread bowl, including the bottom corners.
Arrange bread bowls on a baking sheet and toast at 375°F for 15 minutes, until the interior is golden and dry to the touch.
Season the chicken with salt and pepper. Heat olive oil in a large skillet over medium-high heat and sear the chicken 4–5 minutes per side, until golden and cooked through to 165°F. Remove to a plate.
In the same skillet over medium heat, melt the remaining 4 tablespoons butter. Add the remaining 4 cloves minced garlic and cook 30 seconds, until fragrant.
Pour in the heavy cream, bring to a gentle simmer, and scrape up any browned bits from the bottom of the pan.
Reduce heat to low. Whisk in the parmesan a handful at a time, letting each addition melt before adding more. Simmer 3–4 minutes, until the sauce coats the back of a spoon.
Return the chicken to the skillet and stir to coat in the sauce.
Divide the chicken alfredo filling evenly among the toasted bread bowls. Top with shredded mozzarella and broil on high for 2–3 minutes, until melted and lightly golden. Garnish with parsley and serve immediately.