Prepare the Beets: Trim the tops and tails off the scrubbed beets. You can peel them now with a vegetable peeler, or roast them with skins on and peel after cooking (this is often easier). If peeling raw, do so carefully. Cut the beets into uniform 1/2-inch cubes or wedges.

Cook the Beets: Place the prepared beet pieces in a medium saucepan. Cover with water, add a pinch of salt, and bring to a boil. Reduce heat and simmer for 20-30 minutes, or until the beets are tender when pierced with a fork. Drain the beets thoroughly and set aside.

Make the Glaze: While the beets are cooking or draining, prepare the glaze. In the same saucepan (or a clean one), melt the butter over medium heat. Stir in the granulated sugar, apple cider vinegar, water, salt, and pepper.

Simmer the Glaze: Bring the glaze mixture to a gentle simmer, stirring until the sugar is dissolved. Let it bubble and thicken slightly for about 3-5 minutes.

Combine and Glaze: Add the drained, cooked beets back into the saucepan with the glaze. Stir gently to coat all the beet pieces evenly. Continue to cook over low heat for another 5-10 minutes, stirring occasionally, until the beets are heated through and coated in a glossy glaze.

Serve: Transfer the glazed Harvard beets to a serving dish and serve immediately.