Preheat oven to 450F. Wash and scrub the beets well. Dry the paper towels. With a mandoline or very sharp knife, thinly slice beets.
Line a large rimmed baking sheet with parchment. In a medium bowl, toss the beets with 2 tbsp oil, salt, and pepper. Arrange on prepared pan, spreading out in even layer. Bake 20 mins.
Remove pan from oven and reduce oven temperature to 325F. Arrange the salmon between the beets, skin-sides down, moving some beets aside as needed.
Brush salmon with the remaining 1 tbsp oil. Season with salt and pepper. Return pan to oven and cook 25-30 min., until beets are tender and salmon is cooked through.
Squeeze juice from the orange over salmon and beets. Garnish with the parsley.