Preheat the oven to 350°F (175°C). Lightly oil a 9x13-inch baking dish with 1 teaspoon olive oil and set aside.
Cook the jumbo pasta shells in salted boiling water until al dente according to package directions. Drain in a colander and set aside to cool slightly.
Heat 1 teaspoon olive oil in a skillet over medium heat. Add the diced onion and cook until softened, about 3 minutes, then add the minced garlic and cook 30 seconds more.
Add the ground beef to the skillet and cook until browned, breaking it up with a spoon. Drain any excess fat.
Stir the Greek yogurt, cream cheese, shredded Parmesan, and grated mozzarella into the cooked meat until the cheeses are well combined and smooth; season with salt if desired.
Make the sauce while preparing the filling: in a saucepan, combine the crushed tomatoes, tomato paste, dried basil, and dried oregano. Heat over medium until warmed through and combined.
Spread 1 cup of the tomato sauce evenly on the bottom of the prepared baking dish.
Spoon the meat-and-cheese filling into each cooked shell and arrange the stuffed shells seam-side up in the baking dish on top of the sauce.
Spoon the remaining tomato sauce over the arranged shells. Cover the dish with foil and bake for 20 minutes. Remove the foil and bake an additional 10 minutes until hot and bubbly.
Remove from the oven and let the dish sit a few minutes before serving.