Transfer it to a 9-inch glass pie dish and press it firmly into the bottom and sides of the pie plate. Then fold/crimp the overhanging dough. Prick the bottom and sides of the pie crust all over with a fork.
Transfer the pie dish to a sheet pan and bake for 15 minutes.
In a large skillet, sauté chicken along with the broccoli and the rest of the vegetables until the chicken is cooked and vegetables are somewhat tender.
Meanwhile, in a large mixing bowl, beat the eggs, then add the milk mixture and the herbs. Add the chicken and vegetable mixture and pour into the par-baked pie crust.
Place quiche on a sheet pan. Cover the edges of the exposed crust with foil to prevent browning too much. Bake until the eggs are set and a knife inserted in center comes out clean. Check after 45 minutes, the quiche will take 45-60 minutes.