Put the beetroot in a bowl, drizzle with 2 tsp oil, season well and set aside.
Squeeze out as much juice as you can from the cucumber in a strainer positioned over the sink. Combine the cucumber, yogurt, garlic, and half of the dill in a mixing dish. Season to taste and combine thoroughly.
Spread the tzatziki on a wide plate to serve. Add the beets, 1 tablespoon oil, parsley, remaining dill, and pine nuts over top. If desired, serve with flatbreads.