Prepare the pie crust according to the package directions. Divide it into 4 equal portions, cover with plastic wrap and refrigerate Preheat the oven to 350 degrees F.
Put the chicken breast in a medium pot and cover with 5 cups of water.
Bring to a boil over medium heat and add salt, to taste. (Reserve the legs and thighs for another use.)
Simmer until the chicken is completely cooked through, skimming any fat that rises to the surface, about 20 minutes. Remove chicken, to a cutting board and when cool enough to handle remove the meat and dice into 1/2-inch cubes. Reserve the broth the chicken was cooked in. (Set aside 1/2 cup for another use.)
In a medium pot heat the canola oil over medium heat. Add the onions, celery, carrots, salt and pepper, to taste, and cook until the onions are translucent, about 5 minutes. Stir in the flour, poultry seasoning, and thyme and cook for 2 minutes, stirring constantly. Slowly pour in the reserved 4 1/2 cups of chicken broth, whisking to remove any lumps. Add the chicken and peas, bring to a boil, then remove from the heat. (Reserve 2 cups for another use.)
Divide the remaining mixture between 4 (14-ounce) ramekins. (Alternately, the pot pie can be made in 1 (9-inch) pie pan.)
Roll out the 4 pieces of pie dough to 1/4-inch thick rounds. Brush the edges of the ramekins with milk. Cover each ramekin with a piece of dough and press around the edges to seal. Cut a steam vent in the top of each piece of dough and brush with milk. Arrange on a baking sheet and bake until the crust is golden brown and the filling is bubbling, about 40 to 45 minutes.