Preheat the oven to 375°F. Place the beets on top of a large sheet of aluminum foil and fold the edges over to create a pouch (the beets should be completely enclosed in foil). Lay pouch on top of a baking sheet to avoid any dripping onto the bottom of the oven and roast until tender, about 1 hour. Let cool.
Once cool, slough away the beet skins with your fingers (or a paper towel) and discard. Cut beets into wedges and transfer to a food processor. Add the garlic, tahini, sour cream, lemon juice, salt and a few grinds of fresh pepper and process until smooth. Taste and season with additional salt and pepper if needed.
Scoop into a small serving bowl. Drizzle a spoonful or two of olive oil over the top of the dip if desired. Serve with pita, crackers or wedges of crusty bread.
Store leftovers in the refrigerator in an airtight container for up to 3 days.