Mix flours together in a large bowl. Make a well in the center, and add the salt, the oil, and egg.
Using a fork, start mixing the egg, allowing the flour to incorporate a little at a time, until the mixture is dry and crumbly.
Add the water a bit at a time, and mix it in as you mixed in the egg. Each time, allow the mixture to become dry and crumbly before adding more water.
The mixture will come together into a dough. Knead the dough until it's soft and smooth, about 6-10 minutes.
Wrap it in plastic wrap and let the dough rest about an hour
Roll out the dough on a lightly floured surface to about 1/8 of an inch thick and use a cookie cutter or the rim of a glass to cut out circles of dough 2 1/2 - 3 1/2 inches in diameter.
Place about 2-3 teaspoons of your filling in the center of each circle, fold over, and crimp with a fork.
Bring a large pot of water to a boil over high heat. Meanwhile, melt butter in a skillet over medium-low heat. Working with about eight pierogi at a time, place them in the boiling water, let it come back to a boil, and boil the pierogi for 5 minutes after they float to the surface.
Once boiled, remove pierogi with a slotted spoon and fry in melted butter until browned on each side, about 2-3 minutes per side.