Cut cabbage in half, though the core. Making a v-cut into the base, remove core and discard. With the cut-side down on the cutting board, slice the cabbage in about ¼ inch strips.

Cut the onion in half, through the root, and remove thin, papery outer layers. Slice onion in half moons, about ¼ inch thick. Separate the rings.

Rinse and drain sauerkraut, squeezing to remove as much liquid as possible.

In a large skillet over medium-high heat, melt butter and heat oil. Add onion and sauté for a couple of minutes, just to start to soften it. Add the sauerkraut and sauté another minute or two.

Add in cabbage, chicken broth, and salt and pepper. It will look like it won’t all fit, but it will wilt and reduce in size.
 Reduce heat to medium.

Stir occasionally, as the chicken broth reduces and the bottom layer of cabbage softens and takes on color. Keep cooking, and turning occasionally, until the cabbage is tender and begins to brown on the edges, 15 to 20 minutes. Season to taste.