Add thinly sliced cabbage and shredded carrots to a large mixing bowl and add sea salt, pepper and bay leaf.
Wash hands thoroughly and start massaging all the ingredients in a bowl. Cabbage will soften and start shrinking in size and release liquid.
Keep massaging and gently squeezing the cabbage for the next 5 minutes.
Add vinegar to a mixing bowl and continue massaging and gently squeezing all the ingredients together. You don't have to add vinegar since the fermentation will occur naturally, it's just going to take a bit longer but I like adding it for the flavor. It also helps cutting the time in half (in case I accidentally forget to start my sauerkraut for next day's meal).
When there is enough liquid to cover the cabbage put the sauerkraut mixture into a half a gallon glass jar and pack tightly. Make sure there is plenty of room for sauerkraut to expand so leave some space between sauerkraut mixture and the jar mouth. Cover glass jar with coffee filter or paper towel wrapped around the opening and secured with a rubber band.
Leave sauerkraut on a kitchen counter in a warm spot away from direct sunlight for proper fermentation for 1-5 days. Then mix and turn sauerkraut using a clean spoon once a day to let it breath during the fermentation process. Make sure it is covered in released fermented cabbage juice. If there isn't enough liquid, put and press a saucer on top of sauerkraut and put something heavy on top, like a mason jar filled with water, securely sealed.
The longer the sauerkraut ferments, the tangier it becomes. Taste it with a clean fork to avoid contamination. When it reaches the desired taste, cover the glass jar with a lid and transfer to the fridge. It should keep for at least 2-3 months refrigerated.
When ready to serve, transfer a serving to a dish and drizzle with extra virgin olive oil.