Whisk together 2/3 cup of the flour and the salt in a medium bowl. Whisk together the milk and eggs in a small bowl, and then mix into the flour just to combine. Let the batter sit at room temperature for 30 minutes.
Position a rack in the lower third of the oven and another in the upper third of the oven and preheat to 400 degrees F. Heat the vegetable oil in a large skillet over medium heat, and then add the sausages and brown all over, without cooking all the way through, about 8 minutes. Transfer to a plate. Drain the excess grease from the skillet and set it aside for making the gravy.
Put 1 tablespoon of the butter into a 6-cup casserole dish and place on the lower rack in the oven until the butter is melted and the pan is very hot, about 10 minutes. Carefully add the sausages and batter into the dish and return to the oven for 20 minutes. Move the dish to the upper third of the oven and cook until puffy and golden brown, an additional 15 to 20 minutes. Sprinkle with the parsley.
Meanwhile, heat 2 tablespoons of the butter in the reserved sausage skillet over medium heat. Add the onion and thyme, sprinkle with pepper, and cook until the onions start to brown, about 10 minutes. Lower the heat to medium low and cook for an additional 10 minutes. Stir in the remaining 1 1/2 tablespoons flour continuously for 5 minutes to cook, and then increase the heat to medium and whisk in the stock and Worcestershire sauce. Gently simmer for 10 minutes, and then discard the thyme and whisk in the mustard, lemon juice and remaining tablespoon butter. Divide the toad in the hole among 4 plates and spoon the hot gravy over the top.
We prefer to use Cumberland sausage which can generally be found at a specialty food store.