Preheat the oven to 180C/350F/Gas 4.
Heat the oil in a frying pan and fry the bacon lardons for 4-5 minutes, or until crisp. Remove from the pan with a slotted spoon and set aside.
In the same pan, fry the onions and garlic on a medium heat for 5-6 minutes, or until softened. Add the cooked bacon, carrots, bitter, beef stock, sugar, corned beef and gherkins. Bring the mixture to the boil, reduce the heat and simmer for 25 minutes.
Remove the pan from the heat, stir in the parsley and season to taste with salt and white pepper. Divide the mixture among four individual pie dishes and set aside to cool completely.
Cut four circles out of the puff pastry that are large enough to cover the pie dishes. Place the pastry on top of the pie dishes and brush with the beaten egg.
Place the pies onto a baking tray and bake in the oven for 20-25 minutes, or until the pastry is crisp and golden-brown.