Peel and cut up carrots and potatoes. Put carrots, potatoes and peas in a pot and steam until just tender. Let cool. Poach chicken cutlets in stock (save stock) until done (about 15 minutes). Remove meat, let cool and cut into 1 inch chunks. Melt butter, stir in flour, brown slightly then put stock into mixture, thicken to gravy, cool.
Assemble pie: Put carrots, potatoes, peas and chicken in pie crust, pour gravy on top. Place second crust on top, flute edges, brush with beaten egg, slice air vent in top crust and bake until medium golden brown 30 to 45 minutes at 350 degrees. (Color is more important than time.)
