Place potatoes into a large pot and cover with salted water. Bring to a boil then reduce heat to medium-low, cover and simmer until tender, about 20 minutes. Drain and allow to steam dry for a minute or two, then mash.
Meanwhile, melt 2 tablespoons butter in a large pot over medium-high heat. Add the bacon and cook until it begins to brown, about 5 minutes. Stir in the onion and continue cooking till translucent, about 5 minutes. Stir in the beef and pork mince; continue cooking until crumbly and no longer pink, about 10 minutes. Finally, stir in the mushrooms, chicken stock, salt, pepper and dill. Cover and cook until the mushrooms soften, about 5 minutes more. Stir in the mashed potatoes then set the filling aside to cool.
Stir the plain flour and self-raising flour together in a large bowl, and make a well in the centre. Add the 2 beaten eggs, salt and enough water to form a soft dough. Knead on a well floured work surface until smooth and pliable. Roll the dough to 3mm thick then cut into 10 cm circles.
Spoon the filling onto one side of each of the dough rounds, then moisten the edges with egg wash or water and fold to create half circles. Press the edges together firmly to seal.
Bring a large pot of lightly salted water to a boil. Drop the pierogi in a few at a time, and boil until they float to the surface, about 2 minutes. Once the pierogi have cooked, remove with a slotted spoon, and dip in cold water, pat dry and set aside on a tea towel or paper towel.
Melt the 3 tablespoons of butter a tablespoon at a time in a large skillet over medium-high heat. Add the boiled pierogi, and cook on both sides until hot and golden brown, about 5 minutes. Serve immediately.