Bring a large pot of salted water to a boil and cook jumbo shells according to package directions (about 9–10 minutes) until al dente. Drain in a colander and rinse briefly with cold water to stop cooking; set aside.
Preheat the oven to 375°F and lightly grease a 9×13-inch baking dish with nonstick cooking spray; set aside.
In a large mixing bowl, combine the shredded chicken, Frank's RedHot sauce (5 oz), cottage cheese (16 oz), and melted butter (1/4 cup). Mix thoroughly until well combined.
Spoon the buffalo chicken mixture into each cooked shell using a spoon or small scoop, and place the stuffed shells seam-side up in the prepared baking dish in a single layer.
When all shells are stuffed and arranged, sprinkle the tops evenly with 1 cup shredded cheese.
Bake in the preheated oven for 15–20 minutes, until the center is hot and the cheese is melted and bubbly.
Remove from the oven and serve warm topped with chopped green onions, if desired.