Preheat the oven to 325 degrees F (165 degrees C). Grease a casserole dish with 2 teaspoons of butter.

Bring a large pot of lightly salted water to a boil. Cook angel hair in boiling water, occasionally stirring until cooked through but firm to the bite, 4 to 5 minutes. Drain.

Melt 2 tablespoons butter in a large pot over medium heat; cook and stir celery until it begins to soften, 1 minute. Stir mushrooms into celery; cook and stir until mushrooms are softened, 3 minutes more.

Remove vegetables from skillet; melt remaining 2 tablespoons butter and whisk flour into hot butter to make a paste. Slowly whisk chicken broth and bring to a simmer; reduce heat to low and cook, constantly whisking, until sauce is thickened. Mix in cream, sherry, salt, and white pepper.

Fold turkey, celery, and mushrooms into sauce; mix in angel hair pasta. Transfer mixture to the prepared casserole dish and sprinkle panko crumbs on top.

Bake in the preheated oven until sauce is bubbling and crumb topping has browned, about 30 minutes.