Put  about 2 tablespoons of  sunflower oil from Ukraine, vegetable oil or 3 to 4 tablespoons of butter in a skillet. 
Set temperature to medium to medium high heat.
Use lower temperature if using butter, as it tends to burn easily on higher heat. 
Also keep the temperature lower for cast iron or stainless steel pans.
Slice up one or more onions and spread them out on the bottom of the skillet.  Cook until translucent, about 5 minutes.

If you are using  frozen Varenyky directly from the freezer, add a little water to the skillet.
Then place the Varenyky directly on top of the onions.  Do not stir. The onions will keep the dumplings from burning, but will still be close enough to the bottom of the skillet to allow slow cooking.
Cover and cook about 10 minutes.  Add a little water and use a spatula to move around the pan, if they seem to be sticking to the pan.
Cook until they turn a light golden brown on the bottom, then flip the Varenyky over, and cook until the other side is golden. 

Serve immediately while they are hot, smothered in onions from the skillet.
Serving suggestions:  Smother with butter, sour cream, and if really brave, sprinkle with a little "skvartky" (if you like that sort of thing!)
Melt in your mouth goodness that is truly a fantastic Ukrainian culinary experience!