For me, few things go as well with beets as balsamic, but I wanted to find a great way to marry those flavors in a beet slaw with a thicker dressing that clung like a real slaw dressing should. —JessicaBakes
For the dressing, I have you reducing a lot more vinegar than you actually need! I assume you will want to maximize the time you put into making the balsamic reduction and therefore make more glaze.
So, pour your balsamic into a heavy pan and add your fresh herbs. Heat pan to high, bring the vinegar to a boil and whisk regularly to prevent burning. Boil until it reduces to about half, 2 to 2.5 hours in my kitchen.
Once your glaze is thick enough to coat the back of a spoon, taste for sweetness and add sugar if you wish. Strain the mixture to remove the herbs and allow to cool to room temperature.
Whisk 2 tablespoons of your cooled balsamic reduction with the greek yogurt and lemon juice. Season with salt and pepper to taste. At this point, you can also add more of the balsamic reduction if it's to your liking!
Coat your beet and carrot slaw with the dressing and serve!