In a food processor, combine beets, chickpeas, garlic, parsley, cilantro, cumin, coriander, and kosher salt.
Pulse until the chickpeas are very finely minced, scraping down the sides as needed.
Scoop out 1 tablespoon portions and roll into balls. Place on a baking sheet and chill for 15 minutes.
Meanwhile, heat avocado oil in a cast iron pan to 375°F.
Fry falafel in batches, spacing them out and waiting 10–20 seconds between each addition. Maintain oil temp between 350–375°F.
Fry until golden on bottom, then flip and cook until evenly browned, about 4–5 minutes total.
Transfer to a paper towel–lined plate. Season with kosher salt.
Plate over a bed of hummus, drizzle with tahini sauce, and finish with flaky salt and smoked paprika.