Add the mushrooms, carrots, onion, celery, bay leaf and garlic to the pan and season everything with some salt and pepper. Cook until the veggies are tender, 7-8 minutes, and then stir in the thyme leaves.
While the veggies are working, place a medium saucepan over medium heat and melt 3 tablespoons butter. Sprinkle the flour over the butter and cook for about 1 minute. Whisk 3 cups of the beef stock into the roux and simmer until thickened, 2-3 minutes. Whisk the Worcestershire and Dijon into the gravy. Season with salt and pepper and reserve warm.
When the veggies in the skillet are soft, add the remaining 1 cup of stock to the pan and stir to remove any bits stuck to the bottom and cook away most of that liquid. Remove the skillet from heat and stir in the peas. Stir the prepared gravy into the mixture and reserve.
Mash the cooked potatoes with the remaining 2 tablespoons butter, milk, about 1 cup shredded Gruyere, chives and horseradish. Stir the egg into the mixture at the very end and stir well to fully incorporate it. Season with salt and lots of pepper.
Slather the mashed potatoes over the mixture in the skillet and top with the remaining Gruyere cheese. Place under the broiler to brown.
Garnish the shepherd's pie with paprika and serve straight from the skillet.