Pre-heat oven to 400 degrees.
Cut off most of the beet root and then wrap each beet loosely in aluminum foil. Place foil-wrapped beets on a baking sheet and place in oven for about 50 minutes, until beets are tender. Be sure to check on them and dribble a small amount of water over them if they appear to be drying out.
Let beets cool to room temperature and then remove skins.
Dice beets and place in a large bowl.
Add cherries, quinoa, diced cucumber, and crumbled feta cheese together in the bowl with the beets.
In a small separate bowl, whisk together lime juice, extra-virgin olive oil, and cracked pepper. Pour dressing over the top of the salad.