In two batches, cook dumplings in a large pot of boiling water until cooked through, 4-5 minutes. Transfer to a plate with a slotted spoon. In a large nonstick pan, heat vegetable oil over medium-high heat. In two batches, cook until browned, about 2-2-1/2 minutes per side. Serve with dipping sauce.
A Note From The Little Lady: At my local grocery store, I wasn't able to buy anything less than 1 lb. ground pork. So, we ended up making close to 50 pot stickers. Granted, we LOVED these, so having the extra in our freezer is not a complaint. But in case you would prefer to make 20 and only 20, plan ahead to use the rest to make meatloaf/meatballs/etc.
Another Note: The only wonton wrappers I could find were squares. Not pleased with the idea of pot sticker "packages" vs. half moons, I used a biscuit cutter to make them circles. Easy enough and well worth it for me.