Prepare cabbage by cutting ½ a cabbage and removing the core. Then cutting it into square pieces. Mince garlic as well. Then thinly slice beef eye round with a very sharp knife. Preheat a large skillet over medium-high heat. Add in olive oil, swirl pan. Add in beef and cook until nicely browned and cooked through. Remove to a bowl including any liquid from the meat (it will help make the sauce later on).
In the browned bits at the bottom of the pan, add butter, garlic and saute for 30 seconds.
Add the wine to deglaze and stir well scraping the bits from the pan. Add the mustard, sour cream and parmesan cheese.
Add the beef back in and then add the cabbage and cook until just starting to wilt.
Cook for 3 or so minutes longer or until the cabbage is cooked but still has a very slight crunch. Taste and add an additional pinch of salt as desired so there is a nice balance of flavors. Serve immediately.