Preheat oven to 350 degrees F (180 degrees C). Heat the olive oil in a skillet over medium heat. Add the leeks, onions, and garlic and cook until onions are just soft.

Prick the potatoes all over with a fork. Microwave for three minutes on high heat, until slightly soft and partially cook. Let cool, then slice into 1/2 inch slices.

Grease a pie dish or casserole dish with butter. Layer the potatoes in the dish and top with the cooked veggies, sliced sausage, and parsley.

To make the cheese sauce, melt the butter in a medium-sized pot over medium heat. Add the flour and cook for about three minutes, or until flour is just beginning to brown. Add the salt, black pepper, and milk and continue to cook until mixture has thickened and sticks to the back of a wooden spoon, about 5-8 minutes. Remove from heat and add the shredded cheese. Stir until cheese has melted.

Pour cheese sauce over the sausage and potatoes. Lay the sheet of puff pastry over the dish, trim the edges if necessary. Whisk the egg and brush over the puff pastry. Cut little slits in the pastry to let steam and air out.

Bake the pie in preheated oven for 1 hour. Broil for a few minutes if necessary to brown the pastry.