Preheat your oven to 400°F (200°C). Slice the top off the head of garlic, drizzle with olive oil, wrap it tightly in foil, and roast for 30-35 minutes until soft and fragrant. Once cooled, squeeze the roasted garlic cloves out into a bowl.
Bring a large pot of salted water to a boil and cook the jumbo pasta shells according to package directions until al dente, usually about 10-12 minutes. Drain carefully and set aside, tossing gently with a bit of olive oil if needed to prevent sticking.
In a large bowl, combine the shredded chicken breast, softened cream cheese, sour cream, roasted garlic, mozzarella, Parmesan, Italian seasoning, salt, and pepper. Mix until well incorporated and creamy.
Carefully spoon the creamy chicken mixture into each cooked jumbo shell. Arrange the stuffed shells in a baking dish, fitting them snugly side by side.
Cover the baking dish with foil and bake at 350°F (175°C) for about 20 minutes. Remove the foil in the last 5 minutes to let the tops brown slightly.
Once out of the oven, sprinkle the chopped fresh parsley over the shells for a fresh burst of color and flavor. Serve hot.