Combine 2 1/2 cups flour, 1 teaspoon baking powder, 1/2 teaspoon salt, 2 teaspoons thyme and sage in a food processor, pulsing until combined. Add in 2 sticks butter, 4 tablespoons at a time, pulsing after each addition until mixture forms coarse texture. Slowly add in 6 to 8 tablespoons cold water while machine is running, 2 tablespoons at a time until dough balls up in processor to one side. Remove dough onto a lightly floured board, cut in half and form into 2 (8-inch) rounds. Wrap each tightly with plastic wrap and place in the refrigerator. Chill for 30 minutes prior to rolling out. Repeat to make second batch of dough.

In large saute pan, melt butter over medium heat; add onions, shallot and celery. Saute until just starting to brown. Stir in flour and saute for 2 minutes. Slowly whisk in hot stock, stirring well. When bubbly and thickened, about 5 to 6 minutes, stir in chopped chicken, carrots and peas, and sage. Season, to taste, with salt and pepper. Remove from heat. Let cool while rolling out dough.

Preheat oven to 350 degrees F. On lightly floured board, cut the rounds of dough in half. Roll pieces into 6-inch rounds, about 1/4-inch thickness. Place a round in the bottom of 4 aluminum pie pans and lightly press the sides and bottom to fit the shape of the pans. Generously top with filling until full and slightly mounded. Top with second piece of crust and pinch seams together. Cut 2 small slits in top. Brush with egg wash. Place on a baking sheet and bake for 1 hour to 1 hour 15 minutes or until tops are golden brown and filling is bubbling.