In a large nonstick skillet, heat the oil. Add the sauerkraut, onions, caraway seeds and a 1/2 cup of water; cook, covered, until the liquid evaporates and the sauerkraut and onions are very tender, about 15 minutes. Remove from the heat and cool completely.

Preheat the oven to 400 degrees. Cut the kielbasa into 2 (8-inch) lengths, then cut the pizza dough in 1/2. On a lightly floured surface, roll out each 1/2 of dough into a rectangle about 2 inches longer than the kielbasa and wide enough to wrap around it. Spoon 1/2 of the sauerkraut mixture down the center of each piece of dough, then place a kielbasa half on the sauerkraut. Fold up the dough to enclose the kielbasa completely, pinching the edges to seal. Transfer to an ungreased baking sheet. Bake until golden, 15 to 20 minutes. Cut into slices; serve warm or at room temperature, with honey mustard on the side.