In a saucepan melt the butter. Add the celery, carrots, onion, garlic and season with salt and pepper. Stir to coat vegetables with butter and cover with a buttered round of waxed paper.
Sweat the vegetables for 5 minutes. Stir in the flour and cook for 2 minutes. Add the gravy, milk, fresh thyme and fresh parsley. Simmer this mixture, stirring occasionally, for 15 minutes.
Add the roast lamb and cooked peas. Correct seasoning. Spoon mixture into a 1 1/2 quart oval baking dish. Spread 2 cups mashed potatoes on top with a spatula. Deeply score crisscross pattern in potatoes.
In a small bowl beat together the egg and milk. Brush glaze over potatoes. Put dish in oven. Bake at 350 degrees for 30 minutes, and then put it under the broiler until the potatoes turn golden.