Prepare the mashed potatoes if you are not using store-bought. Keep warm and set aside. If using store-bought, remove from the container and heat until warm.
If making your own, peel the potatoes and cut into 1-inch inch cubes. In a pot of boiling water, add the potatoes and cook for 20 minutes or so, until tender with a fork.
Drain the potatoes and return to the pot; mash with a potato masher and add the butter and milk; season with salt and pepper to taste. Mix together until smooth and set aside.
Make the meat mixture:
In a large skillet, brown the ground beef until cooked through; drain off any fat.
Add the onion, carrots, and celery, and cook until softened, approximately 5 minutes.
Next, add tomato paste, garlic, thyme, cornstarch (or flour), and celery salt. Cook for one minute. Mix well and pour in the Guinness beer and add the Worcestershire sauce.
Stir and cover the skillet with a lid, reduce the heat to low, and simmer for 10-15 minutes.
Preheat the oven to 375 F.
After simmering, stir the peas into the beef mixture. Spoon the mixture into an 8x8 baking dish (approximately 8×8 inches).
Spread the mashed potatoes on top, to completely cover the meat mixture. If you prefer, you can take a fork and make a fun design on top of the mashed potatoes. They will be stacked high.
Sprinkle lightly with a small amount of paprika.
Bake until the top of the potatoes start to brown, and the meat mixture is heated through, for 20 minutes. Remove from the oven and add a sprinkle of fresh chopped parsley.