Step 1In a large skillet, heat the oil over high heat. Stir in 2 cups onions and 1 cup each celery and bell peppers. Saute the vegetables until caramelized, stirring frequently, about 10 to 12 minutes.
Step 2Stir in the andouille and cook until the meat is browned, about 5 minutes, stirring frequently. Stir in the remaining 2 cups onions, 1 cup celery and 1 cup bell peppers, along with the butter, garlic and Tabasco. Reduce heat to medium and cook about 3 minutes, stirring occasionally to marry the flavors.
Step 3Stir in the stock and bring to a simmer; continue cooking until the oil rises to the top (until the water evaporates), about 10 minutes. Stir in the bread crumbs and remove from heat.
Step 4Place the dressing in a baking dish, cover and refrigerate until chilled before stuffing. (To bake the dressing on its own, place it in an ungreased 8-inch-square baking dish; bake uncovered in a 425-degree oven until browned on top, about 45 minutes, stirring and scraping the pan bottom very well every 15 minutes.)