In a large skillet, heat the olive oil over medium heat. Add the chopped onion and sauté for about 3-4 minutes until softened. Add the minced garlic and cook for an additional 1 minute until fragrant.
Add the ground chicken to the skillet, breaking it apart with a spatula. Cook until the chicken is no longer pink, about 5-7 minutes.
Stir in the Italian seasoning, salt, and black pepper. Pour in the Alfredo sauce and mix well. Allow the mixture to simmer for about 5 minutes, stirring occasionally, until heated through.
While the chicken mixture is simmering, toast the hamburger buns in a separate skillet or under the broiler until golden brown.
Once the chicken mixture is ready, spoon a generous amount onto the bottom half of each toasted bun. Top with shredded mozzarella cheese and place the top half of the bun on each.
Serve immediately, garnished with chopped parsley if desired.