In a large saucepan, heat the vegetable oil until shimmering. Add the red bell pepper, chopped onion, celery, chopped garlic and cayenne. Season the vegetables with salt and pepper and cook them over moderately high heat until they are softened, about 2 minutes. Add the sausage to the vegetables and cook, stirring occasionally, until lightly browned, about 5 minutes. Sprinkle the flour on top of the sausage and vegetables and stir until evenly coated. Add the chicken stock and thyme sprigs and simmer over moderate heat for 10 minutes.