In a medium, enameled cast-iron casserole, heat the olive oil. Add the andouille and cook over high heat, stirring occasionally, until lightly browned, about 3 minutes. Transfer to a bowl.

Add the onion, bell pepper, celery, and garlic to the casserole. Cover and cook over high heat, stirring occasionally, until softened, about 3 minutes. Add the Old Bay, rice, and andouille and cook, stirring occasionally, until the rice is opaque, about 2 minutes. Add the stock, water and thyme, season lightly with salt and pepper and bring to a boil. Cover and cook over very low heat until the rice is tender and the liquid is absorbed, about 15 minutes. Fluff with a fork and stir in the crab and scallions. Cover and let stand for 2 to 3 minutes, just until the crab is hot; discard the thyme sprig. Serve in bowls, passing hot sauce at the table.