Cut the cabbage into quarters and remove the core. Thinly slice the cabbage into shreds about the thickness of a quarter.
Place the cabbage in a large mixing bowl. Sprinkle the salt and caraway seeds over the top and toss until evenly distributed.
Pack the cabbage firmly into a clean quart jar, pressing it down with a fermentation tamper as you work. Place a fermentation weight on top and cover with a fermentation lid. If using a regular canning lid, screw it on loosely to allow fermentation gases to escape.
After 24 hours, remove the lid and fermentation weight. Pour in the white wine, then replace the weight and lid, keeping the cabbage beneath the liquid.
Check the sauerkraut every 2 days. Remove any scum from the surface, wash the fermentation weight, and return it to the jar. Replace the lid and continue fermenting.
Begin tasting the wine sauerkraut after 2 weeks. When it has a tart, full flavor and pale golden color, transfer it to the refrigerator or another reliably cold location for storage.
Notes
Use fresh, firm cabbage for the best texture and natural moisture content.
Choose a dry white wine rather than a sweet variety.
Leave some headspace in the jar to allow for expansion and bubbling during fermentation.
Set the jar on a small plate or shallow dish to catch any brine that may bubble out.
Keep the ferment out of direct sunlight in a location with a relatively stable temperature.
Fermentation progresses faster in a warmer kitchen and more slowly in a cooler one, so use flavor rather than time alone to determine when the sauerkraut is ready.
Always use clean utensils when handling the sauerkraut during fermentation.
If the liquid level drops below the cabbage, add salt brine rather than plain water (½ teaspoon pickling salt dissolved in ½ cup water) to keep the cabbage submerged.