Remove beets from oven, splash them in cold water or an ice bath, then let them cool down, so they're easy to handle.
Wear thin kitchen gloves if you don't want your hands to be stained red for a while. Sort of rub the skin off the beets. What ever doesn't come off easily, simply peel or cut off.
Slice beets so you get about five slices per beet. Be careful not to get any broken slices, so don't try to make them too thin. Each slice should be about 1/4 thick.
After slicing, marinate the beets in aged balsamic vinegar, in a medium to large bowl for an hour or so.
Just before slicing the beets, take goat cheese out of fridge and carefully slice it, so that you'll have as many slices of goat cheese, as slices of beets.
Prepare to make a little tower out of the slices from each beet. Put the first beet slice on a small plate and spread it with the goat cheese. Take the next beet slice in your hand and carefully cover it with goat cheese, then add it to the tower of beet slices and goat cheese. When you get to the last beet slice, don't spread it with goat cheese, just use it to top the tower and cover the last spread of goat cheese.
Repeat the above, for the second beet.
Put both sliced beet towers into the fridge for several hours or overnight.
About an hour before your guests arrive, take the towers out of the fridge.
Wash a few leaves of arugula, then mop them dry with paper towels. Divide the arugula into four servings and put them the small salad plates you will serve the beets. Add one glug of aged balsamic vinegar over the arugula.
Carefully, right down the middle, with a steady hand and a sharp knife, cut each beet tower. Carefully, place each striped half over the arugula on each salad plate. Sprinkle just a few chopped pistachios on top and more over the arugula.
Put each salad plate on table and call guests for dinner.