Pre-heat oven to 375oF (190oC). Melt the butter in a large saucepan over medium high heat, add onions and cook until lightly caramelized, approx. 7 to 8 minutes. Add the carrot, parsnip, celery, garlic, savory and seasonings, and sauté until vegetables are softened, approx. 4 to 5 minutes.
Add the flour and mix, coating the vegetables evenly. While stirring, add the broth, then bring to a gentle simmer, and cook until the vegetables are tender and the broth has thickened, approx. 10 minutes. Add the turkey, peas, corn, mustard and thyme, and mix to combine. Taste and adjust the seasoning if needed.
Transfer the mixture to a 9 inch (23 cm) casserole dish. Brush the edges of the casserole with beaten egg and top with the pie crust, pressing onto edges of dish. Brush the top of the crust with the beaten egg, then bake in the centre of the oven for 30 minutes until the crust is golden and the filling is bubbling. Let sit for a few minutes before serving.
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