Place the cubed potatoes into a large pot and add enough water to the pot so that it is about an inch above the potatoes. Bring to a boil for 15 minutes or until potatoes are fork tender. Drain and place back into the pot off of heat.
While the potatoes are boiling, place the ground beef into a large skillet and cook on medium-high heat while breaking up into chunks with a spatula until almost browned. Drain any excess grease. Add the vegetables, except for the peas and cook until they are soft. Add butter and stir until melted. Add in the flour by sprinkling 1 tablespoon at a time while mixing after each tablespoon. Deglaze the pan with broth, wine, and Guinness while scraping up any bits off of the bottom. Add Worcestershire sauce and spices, stir. Simmer for 15 minutes on medium-low. Add peas and continue to simmer until the peas are soft and the sauce is thick (about 10-15 more minutes).
While the meat and vegetables are simmering, prepare the mashed potatoes. Add butter, milk, ½ cup of shredded cheese, salt, and pepper to the potato cubes. Mash with a masher or hand mixer until well blended. Add parsley and chives and mix well.
Preheat the oven to 350 degrees F. Lightly grease a 9×13 inch baking dish. Pour the meat mixture into the bottom of the dish. Spoon the mashed potatoes gently over the meat mixture, being careful not to bring the meat mixture to the top. Press the mashed potatoes down with a spoon to create little peaks on top. Sprinkle the remaining cheddar cheese on top.