Place an oven rack on the lowest position and heat the oven to 425 F degrees
Melt butter in a medium-sized pot over medium heat.
Add onions, garlic, carrots, celery, salt, and pepper. Cook until vegetables are slightly soft for 5 minutes.
Add the mushrooms, sage, and thyme.
Add flour and cook, stirring continually until golden brown for 2 minutes.
Slowly stir in the cream and chicken broth and bring to a boil on medium-high heat.
Stir in the shredded Fontina cheese (optional).
Stir in the potatoes and peas.
Reduce heat to medium and simmer until the sauce is thick and the potato is tender, about 10 minutes.
Take the pot off the heat and stir in the chicken. Add a few more tablespoons of cream if the sauce is too thick.
Place one layer of pie dough on the bottom of the largest pie pan you have -- if you don't have a larger pie pan, then this will make one regular pie size plus one small pie or small casserole. It is a LOT!
Roll out the second, top layer of pie dough and then very loosely place it around the rolling pin. Take it over the pie dish with filling and gently 'unroll' this dough onto the filling.
Trim overhanging extra dough to about ½" from the edge of the pie dish.
Pinch the bottom layer of pie dough with the top layer of pie dough with your fingers, pressing the two layers of pie dough firmly together.
Cut four 2" long slits on top of the pie dough.
Brush the top of the pie and edges with beaten egg.
Place the pie on a baking sheet or pizza pan.
Bake until the top is light golden color, 20 minutes.
With aluminum foil cover the edges of the pie crust or use a pie crust shield to prevent the edges from becoming too brown.
Reduce oven temperature to 375 F degrees, rotate the pot pie, and bake for another 10 minutes until the top crust is a deep golden brown.
Allow the pie to set and cool on a wire rack for at least 45 minutes.