Start by mincing the 2 garlic cloves and chopping the 2 tablespoons of fresh basil. In a large bowl, combine the 1 1/4 cups ricotta (make sure to drain it well if it's watery—this prevents a soggy filling), 3/4 cup shredded chicken, 4 oz goat cheese, 1/2 cup freshly grated Parmesan, 1 egg, the minced garlic, basil, 1 tsp salt, 3/4 tsp Italian seasoning, 1/4 tsp pepper, and 4 oz mozzarella. Mix until well combined and set aside. I always use freshly grated Parmesan rather than pre-shredded because it melts more smoothly and distributes the saltiness better throughout the filling.
Preheat your oven to 375°F. Bring a large pot of salted water to a rolling boil and add the 22 jumbo pasta shells. Cook for 8-10 minutes until al dente (they should have a slight firmness since they'll cook again in the oven). Drain the shells and rinse them with cold water to stop the cooking process. Lay them out on a clean towel to dry slightly while you prepare the sauce.
Dice the 1 small onion and chop the 7 oz sun-dried tomatoes. Heat 1 tablespoon of the oil from the sun-dried tomato jar in a large saucepan over medium heat, then add the diced onion and cook until softened, about 2 minutes. Add the sun-dried tomatoes and cook for another 3 minutes to warm them through and release their flavors. Pour in the 28 oz marinara, 1/4 cup water, 1/2 tsp dried oregano, and 1/4 tsp red pepper. Stir well and simmer for 15 minutes to allow the flavors to meld and deepen. I prefer sun-dried tomatoes packed in oil (like Mezzetta) because they have a richer flavor and better texture than dry ones.
Transfer the chicken filling from Step 1 into a piping bag (or a zip-top bag with one corner cut off for a makeshift piping bag). Pipe the filling into each cooked shell from Step 2, filling them generously but not overstuffing. Spread about half of the sun-dried tomato sauce from Step 3 across the bottom of a 9x13 inch baking dish. Arrange the stuffed shells seam-side up in the dish in a single layer, then pour the remaining sauce over them, making sure each shell is well covered.
Before baking, stir the 1 cup whipping cream into the sauce that's already in the dish—this gives the dish its signature rich, velvety texture. Cover the baking dish tightly with foil and bake at 375°F for 30-35 minutes until the shells are heated through and the sauce is bubbling gently at the edges. Remove the foil and top the entire dish with the remaining 4 oz mozzarella, spreading it evenly over the shells.
Turn on your broiler and place the baking dish on the middle oven rack. Broil for 2-4 minutes, watching carefully, until the mozzarella is melted and lightly browned. Remove from the oven and let rest for 2-3 minutes before serving. Garnish with fresh basil if desired and serve immediately while the shells are still warm and the sauce is creamy.