Trim and scrub the beets very well. Place in a pot with ample water and bring to a boil. Reduce heat and simmer until you can pierce them easily with a fork, about 30 - 40 minutes. Remove, drain and save 1 ½ cups of the cooking liquid. Set the beets aside to cool.

Strain the liquid through a fine mesh sieve and transfer to a small saucepan. Add the balsamic, honey or grape molasses and a pinch of salt and pepper. Simmer until reduced to a thin syrup. Set aside.

Peel the beets. Cut each beet into 4 – 6 rounds. Season lightly with salt and pepper.

To serve: place a teaspoon of the taramosalata on each of 6 serving plates. Place a beet round on top. (You may have to discard the very first round slice if it is not flat enough to hold up the ensuing stack of slices steadily.) Place a heaping teaspoon of taramosalata over the first slice, then a beet round, another teaspoon of taramosalata, and continue so that each beet is a stack of alternating layers, beet, taramosalata, beet, etc. The top layer should always be a beet slice.

Season lightly with salt and pepper. Drizzle a little of the reduced beet syrup and olive oil over and around the beets. Garnish, if desired, with a sprig of dill.