To prepare the chicken and dumplings with biscuits recipe, you will first need to prepare your ingredients. In a large skillet, heat the oil over medium-high heat. Add the onion and cook, stirring frequently, until the onions are translucent, about 5 minutes. Stir in the flour, salt, pepper, and thyme. Cook the mixture, whisking constantly, for 1 minute. Remove the skillet from the heat and add the drained chicken, sour cream, Worcestershire sauce, cream of mushroom soup, cornstarch and milk. Bring to boil, then reduce heat to low and simmer for 30 minutes, or until chicken is no longer pink. Serve warm.