Preheat oven to 200 °C (400 °F).

In a large skillet set over medium heat, sauté onion and garlic in oil, without browning. Add cumin and stir for about 1 minute. Transfer the mixture to a food processor.

Add chickpeas, beets, breadcrumbs, eggs and tahini. Season with salt and pepper to taste. Pulse until you obtain a coarse purée.

Using your hands, shape mixture into approximately 20 small balls and place them on a parchment-lined baking sheet. Brush falafels with remaining olive oil. Bake until crisp and heated through, about 30 minutes.

While falafels are cooking, prepare sauce by combining yogurt, lemon zest and juice and half the mint and parsley in a small bowl.

Spread yogurt sauce over each pita, then add falafels, radishes, cucumbers and remaining parsley and mint.