Place a 12-inch cast-iron skillet in oven, and preheat oven to 500 degrees Fahrenheit. (Do not remove skillet while oven preheats.)
Heat one teaspoon oil in a large nonstick skillet over medium-high. Add onion; sauté two minutes. Add carrot, corn , and peas; sauté one minute. Remove mixture from skillet; set aside.
Add flour and one tablespoon oil to nonstick skillet. Cook 30 seconds, whisking constantly. Slowly add stock, then the cream stirring constantly. Bring to a boil; reduce heat and simmer, whisking often, until mixture is thickened, about three 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 five minutes. Remove from oven; increase heat to broil.
Top pizza crust with half cup stock mixture. Sprinkle with onion mixture, chicken, and cheese. Broil until cheese is melted, about two minutes. Drizzle with remaining stock/cream mixture. Garnish with thyme, and adjust seasoning with fresh pepper, and salt.