Wash beets thoroughly in cold water (use a vegetable scrub brush if needed). Drain and gently pat dry.
With a sharp knife, carefully trim root and stem end of beets, removing anything unappealing. Add beets to pot of cool, clean salted water and cook on medium heat until tender. Drain, cool and peel outer skin as needed. Slice the beets about 1/4" thick.
In a pan large enough to fit the beets, melt 1/2 stick unsalted sweet butter. Add beets and saute until hot, adding more butter if needed.
To serve, arrange arugula on a plate, top with beets and drizzle with contents of pan. Season with salt and pepper to taste.
