Preheat your oven to 375°F and lightly grease a 9x13 inch baking dish with butter or cooking spray. While the oven heats, bring a large pot of salted water to a rolling boil. Add the jumbo shells and cook according to package directions until just al dente (usually 9-11 minutes)—they should still have a slight firmness since they'll continue cooking in the oven. Drain the shells in a colander and lay them out on a clean kitchen towel to cool slightly and prevent sticking.
In a large bowl, combine the softened cream cheese, cottage cheese, and sour cream, stirring until smooth and well blended. Add the shredded chicken, parmesan cheese, 1 cup mozzarella cheese, parsley, garlic powder, and Italian seasoning. Mix everything together thoroughly until the filling is even and creamy throughout. I like to taste a small spoonful here to adjust seasonings—the filling should be flavorful but not oversalted since the alfredo sauce adds richness too.
Using a small spoon or a piping bag, carefully fill each cooked shell with the creamy chicken mixture from Step 2, working gently to avoid tearing the delicate pasta. Arrange the filled shells seam-side up in the prepared baking dish, packing them snugly so they hold their shape and don't tip over during baking. I find that laying them out in neat rows makes the dish look more polished, plus it ensures even cooking.
Pour the entire 15 oz container of alfredo sauce evenly over the filled shells, making sure each one gets coated. This sauce is your flavor carrier and will help keep everything moist and delicious. Sprinkle the 3/4 cup of freshly shredded mozzarella cheese evenly across the top—freshly shredded cheese melts better and more smoothly than pre-shredded varieties, which contain anti-caking agents that can affect the texture.
Place the baking dish in the preheated 375°F oven and bake for 30 to 35 minutes, until the sauce is bubbling around the edges and the cheese on top is golden brown and melted. The shells should be heated through and the filling set. If the top is browning too quickly before the filling is heated through, loosely tent the dish with foil for part of the baking time. Let the dish rest for 5 minutes after removing from the oven—this allows everything to set slightly and makes serving easier.