In a large skillet, warm the butter over medium-high heat until bubbling and lightly browned, about 2 minutes. Add the sauerkraut and toss to coat. Lower the heat to medium. Spread the sauerkraut evenly in the pan and cook, stirring occasionally, until it begins to brown around the edges, about 10 minutes.
In a measuring cup, stir the vinegar with the mustard and honey until combined. Remove the skillet from the heat, add the dressing and toss to coat. Garnish with the parsley and serve.