Cook pasta shells in salted, boiling water until al dente. Drain and set aside.
Pour 1 cup/245 g tomato sauce into the bottom of a 9x13-in baking dish.
Combine Chobani, ricotta, 1 c mozzarella, ¼ c parmesan and parsley in a medium bowl. Stuff each shell with Chobani mixture and arrange seam-side down in baking dish. Top with remaining sauce and cheeses.
Heat broiler to high. Broil stuffed shells until warmed through and cheese is melted and bubbling, 6-8 minutes. Serve.