Wash beets well and slice in half or quarters to make 1-2 inches thick. Place in medium sized cooking pot with 2 inches of water, or enough to just cover the beets. Boil for 20-25 minutes or until al dente, soft but slightly firm to the bite. Drain and let cool. While beets are cooking prepare the caramelized onions.
For the caramelized onions:
In a large cast iron or heavy bottomed frying pan, heat butter and onions over low/medium heat. Sprinkle salt over onions. Cook onions for 15-18 minutes until they begin to turn dark yellow/light brown, stirring every 2-3 minutes to prevent burning, lowering heat if necessary. Don't walk away from these, stir every 1-2 minutes the last 5 minutes of cooking as they can burn quickly.Cool completely.
For the balsamic miso dressing:
In a small mixing bowl combine olive oil, balsamic vinegar, miso, sugar, and ground ginger and mix well. Transfer to serving container such as a glass jar or pour directly over salad if serving immediately.
Assemble the salad:
In a large serving bowl, layer the leafy green salad mix with cabbage, grated carrot, and feta cheese on top with the cooled caramelized onions.
Carefully peel cooked and cooled beets and slice thinly, then gently mix into salad.
Drizzle with balsamic miso dressing if serving immediately or serve with dressing on the side.
Notes
Mellow White Miso can be found in Whole Foods markets or ordered online on Amazon. This salad can easily be prepared ahead by cooking the onions and beets the day before and adding them right before serving.