First, make the dough. Place the flour and salt in a bowl and in a separate bowl prepare wet ingredients. Whisk the egg into the milk and then whisk in the oil. Add the wet ingredients to the dry ingredients immediately and stir the dough to combine. Keep mixing until no dry patches remain and the dough has a homogenous consistency (the dough can be mixed by hand or on a stand mixer). Set dough aside to rest from 1 hour up to a day.
For the filling, peel and chop potatoes and trim broccoli bottoms. Grate cheddar if you do not have pre-grated cheese.
Boil the potatoes in salted water for 20 minutes or until soft enough to mash, strain and reserve. Mash the potatoes while still warm, adding cheddar to the mix and melt through and season with salt and white pepper. Briefly boil the broccoli in salted water for 1-2 minutes to cook and tenderize and then shock in ice water to stop cooking and preserve the bright colour. Chop the broccoli down to a rough approximation of a small dice and mix through the mashed potato and cheese mixture.
To make the perogies, roll out the dough on a floured surface with a floured rolling pin to ¼ inch thickness and then punch out rounds with a cookie cutter or a cup. The rounds should be 3-4 inch wide. Gather your scraps and reroll and re-cut them to get more rounds after until all the dough is used up. To fill the perogies place a tablespoon of filling in the center of the dough rounds, dampen the edges of the dough with a fingertip or pastry brush and then fold over and press to stick together. You can crimp the edges sealed with a fork or your fingers for decoration, your choice.
To cook, gently place perogies in boiling, lightly salted water and boil for 2-3 minutes or until perogies are floating. Drain the perogies and serve with sour cream and any other accompaniments that you like.
***Boiled perogies are traditional and quite nice on their own, but searing them in warm butter or olive oil to get crispy edges makes them crunchy out the outside and irresistible. Serve with sour cream for certain, but add your choice of bacon bits, garlic sausage, sauteed onions, chopped green onions or hot sauce.***