In a large dutch oven, brown the chopped bacon over medium high heat. Transfer crisped bacon to a paper towel lined dish. Set aside.
In two or three batches, brown lamb in dutch oven, using bacon fat to sear the meat. Use tongs to turn the chunks of lamb over and brown all sides.
Add all the lamb back to the pot and stir in the leeks, celery and onion. Cook over medium heat for 3-4 minutes until vegetables begin to soften. Add the chunks of parsnips, carrots and potatoes.
Knot a piece of string around the thyme and rosemary and add to the pot. Add bay leaves, broth and stout. Heat just to boiling, place the lid tightly on the pot and transfer to the oven. Braise for 2 1/2 hours.
Remove pot from the oven and stir in the cornstarch and water mixture to thicken sauce slightly. Add the peas and pearl onions, stir to combine and place the lid back on the pot to warm them through. Sprinkle with chopped parsley and reserved bacon.