Place beets, onion, and garlic on a large piece of aluminum foil. Drizzle a little olive oil over everything, season with a little salt and pepper, tossing to coat.
Foil foil edges up to create a pouch around the beets.
Roast at 375 for about 1 hour, or until beets are quite tender.
Allow to cool slightly, then rub the skins off the beets with some paper towels (or your bare hands – expect some staining!).
In a food processor or blender, blitz roasted beets, onion, and garlic together with remaining ingredients until smooth. Transfer to a large pot.
Bring ketchup just to a boil, reduce heat to medium-low, and simmer for 20 minutes or so, until thickened to desired consistency.
Remove from heat, cool to room temperature before transferring to jars or bottles. Chill.
Notes
* I used red wine vinegar, but cider vinegar would also taste wonderful. In a pinch, use regular white vinegar