Preheat the oven to 350°. Melt 2 T. butter in a deep skillet over medium heat. Add onion, carrot, and celery. If adding potato, peel it and cut into ½" dice. Add to the skillet and cook until all vegetables are soft.
Sprinkle the flour over the cooked vegetables and stir for one minute. Add the wine and stir a minute more, scraping any bits off the bottom of the pan. Add the chicken broth a little at a time, stirring as the sauce thickens. when the sauce is smooth, stir in half and half. Fold chicken and peas into the sauce. Taste and adjust seasoning as necessary
If using a refrigerated crust, follow the directions on the box, unroll and fit into a pie pan. Crimp the edge. If using a frozen crust, no need to thaw or crimp. Pour the chicken and sauce into the prepared crust.
Melt the remaining 2 T. of butter. Toss well with the stuffing crumbs. Sprinkle over the top of the pie. Bake for 20 -to 30 minutes until the crust and crumbs are browned and the filling is bubbly.