If using canned beets, drain them well and set aside. If using fresh beets, trim the greens leaving about 1 inch of stem, rinse well, then place in a pot and cover with water. Add 1 teaspoon salt and bring to a boil. Simmer 30–45 minutes, or until a knife slides in easily. Cool just enough to handle, slip off the skins under cool running water, then slice or cube and set aside.
In a small bowl, whisk the cornstarch with the 1/2 cup water until completely smooth with no lumps. Set near the stove.
In a medium saucepan, combine the sugar, apple cider vinegar, kosher salt, black pepper, and, if using, a pinch of ground cloves or allspice. Warm over medium heat, stirring until the sugar dissolves and the mixture comes to a light simmer.
Whisk the cornstarch slurry again, then slowly pour it into the hot vinegar-sugar mixture while stirring constantly. Keep the heat on medium and cook, stirring, for 2–4 minutes, until the sauce thickens and looks glossy. If it becomes too thick, whisk in a tablespoon or two of water.
Gently add the sliced or cubed beets to the thickened sauce and stir to coat evenly. Bring to a gentle simmer and cook for 5–10 minutes, stirring occasionally, until the beets are heated through and have absorbed some of the sweet-and-sour flavor.
Reduce the heat to low and stir in the butter until fully melted and incorporated. Taste carefully. For more tang, add 1–2 teaspoons fresh lemon juice or an extra splash of vinegar. For more sweetness, stir in 1–2 teaspoons additional sugar. Adjust salt and pepper if needed.
Remove from the heat and let the beets rest 10–15 minutes to allow the flavors to meld; the sauce will thicken slightly as it cools. Before serving, garnish with chopped fresh parsley and/or orange zest if desired. Serve warm or at room temperature.