Wash the beets and trip the ends to about ½ an inch (I held onto this little part later to remove the skin.)
Place them in a casserole dish and add about 1-inch of water. Cover (lid or foil) and bake on 400 degrees for 45 minutes.
When tender enough to stick a knife through, remove from oven and remove skins. Chop and place in a bowl with balsamic vinegar, salt, and pepper.
Let the beets marinate for 15-30 minutes, then add 1 tablespoon olive oil. (According to the pros, if you add the olive oil earlier, the beets won’t be able to absorb the vinegar. So just wait.)
Sprinkle 1 tablespoon olive oil over arugula and toss well. Top with beets and feta cheese and serve.