In the large skillet, melt the butter with the olive oil over medium-high heat. Add the chopped onion and sauté until golden, 7 to 8 minutes. Add the mushrooms, salt, and pepper, then sauté until browned and tender, about 4 minutes. Add the sliced carrots, cover, and cook until carrots soften slightly, about 2 minutes. Add diced turkey, gravy, thyme, and rosemary.
Bring the filling to a boil, then reduce heat to low and simmer to thicken if necessary. You don't want it runny or it will make the bottom crust mushy. Season to taste with salt and pepper. Mix in the peas and chopped parsley. Pour the filling into the prepared pie crust and refrigerate until cool, about 30 minutes.
Place the top crust in place and fold the edge of dough over edge of pie dish. Tuck the edges under and crimp with a fork. Cut miniature leaves and arrange them on top. Chill 10 minutes.
Lightly brush top of pie with glaze. Make four slits in center of pie to allow steam to escape. Bake pie until crust is golden and filling is bubbling, 30 to 35 minutes. Remove from oven and let cool 10 minutes. Serve with leftover cranberry sauce.