Place a large pot of water over high heat and bring up to a boil. Once boiling, add some salt and cook pierogies according to package directions. Just before draining, remove and reserve about 1/2 cup of the cooking liquid. Drain and reserve the pierogies.
Once you have the water on for the pierogies, preheat a large skillet over medium-high heat with 2 tablespoons of butter and 2 turns of the pan of EVOO, about 2 tablespoons. While the skillet is heating up and the butter melting, combine the flour and paprika in a large dish. Season the chunks of chicken with salt and pepper, dredge them in the flour-paprika mixture and shake off any excess.