To make the dough, mix all the ingredients in a bowl and knead until smooth. You may need to add more water. Set aside and cover with a clean, dry towel for 30 minutes.
While the dough is resting, heat the oil in a large pan over medium heat. Add the garlic and sauté until fragrant. Add the onions and cook until translucent. Then, add the carrots, celery, potatoes and seasonings.
Stir well to combine and cover, venting the lid slightly. Check on the vegetables after a few minutes. If they seem to be browning quickly, turn the heat down a bit. Stir every few minutes and check the potatoes for doneness. Once they are fork-tender, add the peas, cook for another couple minutes, and turn off the heat.
Dust a work surface with flour and roll out half of the dough as thin as you can get it. Using a cookie cutter or the can from the peas, cut out circles and set aside. Knead the leftover dough into a ball and roll out again. Do this again with the other half of the dough until it is all or mostly used up.
Take a circle of dough and roll out a little more with your rolling pin to make it thinner and wider. You'll be able to use more filling this way. Dip your finger in water, and wet the edges of half of the circle. Spoon on some of the filling, and pinch the pocket shut, forming a half moon.
Once all of the pierogis are stuffed and sealed, bring a pot of water to a boil. As it comes to a boil, get a large pan ready to fry the pierogis. Turn the heat to medium and add 2-3 tsp of margarine to the pan to melt.
Once the water is boiling, drop in as many pierogis as you think will fit into the frying pan. Usually 8-10 at a time is ok. When they rise to the top, skim them off and drop them into the heated frying pan. Cook for about 3-5 minutes on each side until browned and crispy. Transfer to a plate and keep in a warmed oven until all of the pierogis are done. Continue to cook in batches, adding more margarine to the pan as needed.