Preheat oven to 375°F. Grease a large baking dish with cooking spray and set aside.
Add butter to a large skillet over medium heat. Once melted, add the onion, garlic, celery and carrots and cook, stirring often, until the vegetables have softened, about 5 to 8 minutes. Season with a pinch of salt, pepper and the thyme and sage. Stir in the green beans and turkey and cook until warmed through, another 2 to 3 minutes.
Transfer to a large bowl, and add the stuffing mix, stock and dried cranberries and mix until well incorporated. Set the mixture aside to cool.
Meanwhile, bring a large pot of cold water to a boil. Season liberally with salt and add the pasta. Cook until almost done, not completely, as it’ll continue to cook in the oven. Drain and set aside.
To make the sauce, add butter to a saucepan over low-medium heat. Once melted, whisk in the flour and cook for about 30 seconds or so. Slowly whisk in the milk and cook, stirring often, until the sauce has thickened. Season with the spices and a pinch of salt and pepper. Remove from the heat and stir in the cheeses until fully melted through.
Pour half of the sauce into the prepared baking dish, spreading it out evenly. Fill each pasta shell generously with the filling and placing it in the dish. Continue until the entire filling is used, you might not need all of the pasta shells (especially since some will be damaged through cooking). Spoon the remaining sauce over the shells and bake until bubbly and golden brown, about 25 minutes. Remove from the oven and garnish with scallions before serving.