Place a 12-inch cast-iron skillet in the oven, and preheat oven to 500°F.  (Do not remove skillet while the oven preheats.)

Heat 1 teaspoon oil in a large nonstick skillet over medium-high.  Add diced onion; sauté for 2 minutes.  Add carrot, celery, and peas; sauté for 1 more minute.  Remove mixture from skillet; set aside.

Add flour and 1 tablespoon oil to nonstick skillet.  Cook 30 seconds, whisking constantly.  Slowly add stock or broth, stirring constantly.  Bring to a boil; reduce heat and simmer, whisking often, until mixture is thickened, about 3 minutes.  Remove from heat.

Place dough on a lightly floured surface; roll into a 12-inch circle.  Very carefully place the dough in the preheated cast-iron skillet; flatten to cover the bottom of the pan.  Bake in preheated oven until crust is lightly browned, about 5 minutes.

Remove from oven; increase heat to broil.  Top the pizza crust with 1/2 cup stock mixture.  Sprinkle with onion mixture, chicken, and cheese.  Broil, about 4-inches from heat, until cheese is melted, about 2 minutes.

Drizzle with the remaining stock mixture.  Sprinkle with thyme, sage, salt & pepper.  Serve immediately.