Add beef and cook until brown, breaking up with a wooden spoon as it cooks.
Combine gravy and water in a 2-cup measure. Stir 1/4 cup of gravy mixture into meat-vegetable mixture. Blend well. Add salt and pepper.
Set oven to (hot) 425 degrees F.
Melt remaining 2 tbsps butter in a 10-inch quiche dish or pie place in oven while it heats (to heat up the butter and quiche dish or pie plate).
In the meantime, beat eggs in medium-sized bowl. Add milk, beat until well blended. Add flour and salt, beat until smooth. Pour into quiche dish or pie plate. Spread meat-vegetable filling evenly over the batter to within 1 inch of edge.
Bake for 30 minutes or until brown and puffy. Heat remaining gravy to serve with the pudding.
NOTE: The yorkie beef pudding will look like a puffed up dough ring around the edge of the dish or plate and the beef-vegetable mixture will be positioned in the centre of the pudding. Serve with mashed potatoes or a salad.