Just made a batch yesterday.
Peel and slice beets.
Add enough water and vinegar to cover the beets in a pot. About 3/4 water and 1/4 vinegar.
Add about 3-4 tablespoon of sugar.
About 1-2 tablespoons of salt.
About 1/4-1/2 teaspoon of black pepper.
Boil for 40 minutes.
Once cool, Add diced onion and the peeled eggs to your container and then add the beets and liquid.
Same recipe my mother used and I use. The brown sugar is an interesting thought.
Incidentally, I after the fall picking, I cut off the tops of beets and layer them in 5-gallon buckets of sand and store them in an attached, unheated garage. Keep the sand moist by sprinkling water on the sand. I picked some from the sand yesterday and most were just as good as they were in October.