Preheat your oven to 375°F (190°C).
Bring a large pot of well-salted water to a boil over medium-high heat. Cook the jumbo pasta shells until just al dente, about 9 to 11 minutes. Drain and rinse under cold running water until cool enough to handle. Set aside.
Season the chicken breasts on both sides with ½ teaspoon salt and ½ teaspoon pepper. Warm the olive oil in a large skillet over medium heat and add the chicken. Cook for about 18 minutes, flipping halfway through, until browned and an instant-read thermometer inserted into the thickest part reads 165°F (74°C). Transfer to a cutting board.
Using two forks, shred the cooked chicken into bite-sized pieces. Set aside.
In a medium bowl, stir together the ricotta, 1½ cups Italian cheese blend, parsley, ½ teaspoon salt, ¼ teaspoon pepper, shredded chicken, and 2 tablespoons heavy cream until well combined. Set aside.
In a large deep skillet, combine 2 cups heavy cream and butter. Bring to a gentle simmer over medium heat and cook for 2 minutes, stirring occasionally. Whisk in garlic, Italian seasoning, and the remaining ½ teaspoon salt and ½ teaspoon pepper. Cook for 1 more minute.
Whisk in 2 cups of the Parmesan until fully melted and the sauce is smooth. Remove from heat.
Spread 1 cup of Alfredo sauce evenly across the bottom of a 9x13-inch baking dish.
Generously fill each pasta shell with the chicken-ricotta mixture and arrange them seam side up in the baking dish.
Pour the remaining sauce over the shells. Sprinkle with the remaining ½ cup Italian cheese blend and ½ cup Parmesan cheese.
Bake for 20 to 25 minutes until bubbly and golden. Garnish with fresh parsley and serve warm.