Preheat oven to 400°. Scrub beets and trim away any scraggly roots. Place them in a small baking dish. Drizzle with olive oil. Cover pan tightly with foil and put in a hot oven. Roast for 25 to 30 minutes, until beets are tender.
Remove from oven and let them cool.
While beets roast, place cashews in a heatproof bowl and cover them with boiling water. Let them sit for at least 30 minutes.
When beets are cool enough to handle, rub away skins and place them in the bowl of a food processor. Drain cashews, reserving soaking liquid, and add them to the beets, along with the Greek yogurt, garlic cloves, lemon juice, salt and pepper.
Run the processor, stopping occasionally to scrape down the sides, until the dip is smooth. If it seems a little too thick, use some of the water from the soaking cashews to thin it out.