Preheat a grill on medium or an oven to 375 degrees.
In a pot of boiling water cook the pierogies according to the directions on the package. Drain and set aside.
In the meantime, in a saucepan on low heat warm the sauerkraut. Stirring occasionally.
If using a grill: cook the kielbasa on both sides to an internal temperature of 150 degrees using a thermometer. If using an oven place the kielbasa on a foil lined baking sheet and cook on both sides to an internal temperature of 150 degrees using a thermometer.
In a nonstick pan on medium heat, melt the butter. Once the butter starts to sizzle, brown the pierogies on both sides until they are golden brown.
Serve the kielbasa with sauerkraut and mustard and the pierogies with sour cream. Crusty bread on the side.