Pour in enough water to cover the beets by 1 inch. Bring to a boil over high heat, then reduce heat to medium-low, cover, and simmer until the beets are easily pierced with a fork, about 10 minutes; drain.
Whisk together the brown sugar, vinegar, water, cornstarch, cinnamon, nutmeg, and cloves in a saucepan.
Add the beets and the butter, turn the heat to medium, and cook, stirring constantly, until the mixture comes to a boil. Cook until the sauce thickens slightly, about a minute or two. The sauce will not be sticky-thick, but will still pour nicely.
