Peel potatoes, cut each in half, and put in 3 qt. saucepan with warm tap water (enough to cover potatoes). Add 1 tsp. salt, 1 chopped medium onion, 1/2 cup of fresh chopped parsley, 1/2 cup of finely chopped celery heart (the part at the center of the celery stalk - use leaves and all).
Bring the water to a boil and cover with lid. Cook for 20 minutes with lid tilted to prevent boiling over. Test with fork for doneness (they should be soft). If potatoes are not soft, cook longer.
Remove potatoes from heat. Drain water off using a sieve. Any onions, celery or parsley that accidentally gets drained should be put back in with potatoes. Add one pound of sharp cheese cut in small pieces (or shred it) to potatoes.
Use a potato masher to mash potato mixture and cheese. Add 1/2 tsp. pepper and then mash like mashed potatoes. If the potato/cheese filling is too stiff, add a dash or two of milk and remash. Set aside to cool.
In a mixing bowl, add 4 cups flour, 2 eggs (slightly beaten with a fork), 1 tsp. salt, 2 tsp. Parkay margarine (room temp.). Mix with your hands until eggs and margarine are crumbly. Add 3/4 cup water a little at a time. You should be able to make a large ball with the dough. If it's too dry, add up to 1/4 cup of more water.
Divide the dough into four smaller balls. Flour your counter so dough doesn't stick. Take out one of the dough balls. Sprinkle flour on top of dough ball and roll with rolling pin until about 1/4" thick.
Cut circles in the dough using a glass jar upside down (the opening in the jar should be about 3-4"). On each circle place one tsp. of the potato filling. Dip your finger in a glass of water and wet entire edge of pierogie using your finger. Fold pierogie and pinch edge shut all the way around.
Using an 8-10 qt. pot, fill with hot tap water about 3/4 full. Add 2 tsp. salt and bring to a rolling boil. Add pierogies one at a time to the boiling water. Boil for about 5 minutes. You can cook about 5 pierogies at a time. When pierogies are done they will float to the top. Remove with a slotted spoon and put on a cookie sheet (they cannot touch each other or they will stick together). Repeat with remaining pierogies. At this point, they are NOT ready to eat.
After they cool, you can wrap each pierogie with saran wrap and freeze for later. Put saran wrapped pierogies in Ziploc bag before freezing. They will keep 6-9 months.
When you are ready to eat pierogies, they must be deep fried. Using a large iron skillet, add canola oil until it reaches 1/4 the way up the side of the pan. Thickly slice an onion and place in the pan. Heat oil. Add pierogies and brown on each side. When the onions get really brown, remove them. Continue frying pierogies (you don't need to add more onion--the oil is already flavored). You may have to add more oil if frying alot of pierogies at a time.
Frozen pierogies can go straight from freezer into oil but be careful of oil spatter.
BE CAREFUL WHEN YOU TURN PIEROGIES. IF YOU POKE THEM THE FILLING WILL OOZE OUT. Use spatula or a slotted spoon to turn.