Start by bringing a large pot of salted water to a rolling boil over high heat. Add the jumbo pasta shells and cook according to package directions until al dente, usually about 8-10 minutes. You want the shells tender enough to stuff but firm enough to hold their shape during baking.
While the shells cook, combine the softened cream cheese, 1 cup of Parmesan cheese, pesto sauce, shredded chicken, and minced garlic in a large mixing bowl. Mix everything together until well combined and creamy, ensuring the pesto distributes evenly throughout. The mixture should be easy to spoon but not too wet or runny.
Drain the cooked shells and let them cool slightly so you can handle them comfortably. Using a spoon or small cookie scoop, fill each shell generously with the pesto chicken mixture. Place the stuffed shells in your greased 9x13 inch baking dish, arranging them in a single layer.
Sprinkle the remaining ¼ cup of Parmesan cheese evenly over the top of all the stuffed shells. This creates that beautiful golden crust we're aiming for. For extra moisture, drizzle a little extra pesto sauce over the shells before baking.
Preheat your oven to 350°F and bake the stuffed shells for about 30 minutes. You'll know they're done when the cheese is melted and bubbly, and the shells are heated through completely.