Place a 12-inch cast-iron skillet in oven, and preheat oven to 500°F. (Do not remove skillet while oven preheats.) Heat 1 teaspoon oil in a large nonstick skillet over medium-high. Add onion; sauté 2 minutes. Add carrot, celery, and peas; sauté 1 minute. Remove mixture from skillet; set aside. Add flour and 1 tablespoon oil to nonstick skillet. Cook 30 seconds, whisking constantly. Slowly add stock, 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. Carefully place dough in preheated cast-iron skillet; flatten to cover bottom of pan. Bake in preheated oven until crust is lightly browned, about 5 minutes. Remove from oven; increase heat to broil. Top pizza crust with 1/2 cup stock mixture. Sprinkle with onion mixture, chicken, and cheese. Broil until cheese is melted, about 2 minutes. Drizzle with remaining stock mixture. Sprinkle with thyme, pepper, and salt.