For the chicken:
Preheat oven to 350°.
Stuff onions and whole carrots into the cavity of the chicken. Rub 1/4 cup salt, black pepper and 1 stick butter into skin of chicken. Place rosemary sprigs under the skin and place into a roasting pan. Place sage on top of chicken and roast for 1 1/2 hours.
Remove the chicken from the oven. Transfer to a cutting board and allow to cool.
For the filling:
Place carrots and potatoes on sheet pan and season with salt and pepper. Place into the preheated oven and roast until caramelized.
When chicken has cooled, discard the onions, carrots, sage and rosemary. Pull the chicken meat off the bones and cut into 1/2-inch pieces. Place into a large bowl with chicken juice from roasting pan along with potatoes, 1 cup sliced carrots, peas, corn, heavy cream and 1/2 cup flour. Mix together well. Set aside for crust. *Cook's Note: Filling will be thick.
For the crust:
Knead 3 cups flour, 2 tablespoons salt, sugar, shortening, water and 1/2 cup melted butter together in a large bowl, slowly adding the water. Divide into 2 pieces and roll out on a lightly floured work surface. One will be the bottom crust, the other the top. Place 1 piece of dough into the bottom of a 9-inch pie dish. Add filling and top with the other piece of dough. Crimp the edges together with a spoon or a fork. Brush the top crust with melted butter and bake in the preheated oven for 50 minutes.