Add chickpeas to a large bowl and cover with at least 2 inches of water. Let soak overnight, then drain.
Add the tahini, water, lemon juice, minced garlic, ½ tsp cumin, cayenne, and ¼ tsp salt to a blender. Blend until smooth, then refrigerate until ready to serve.
Combine chickpeas, whole garlic, parsley, 1 tsp cumin, onion, hot pepper flakes and 1 tsp salt in a food processor. Pulse until blended but still a bit chunky.
Sprinkle in the baking powder and 4 tablespoons of the flour, and pulse until combined. Transfer to a bowl, cover and refrigerate for at least 2 hours.
Form mixture into 1 inch balls.
Heat 3 inches of oil to 375ºF in a deep pot or wok and fry 1 ball to test. If it falls apart add a little flour. Gently lower 6 falafel at a time into the hot oil and fry until deep golden-brown, flipping them halfway through, 5 to 7 minutes total per batch. Remove the cooked falafel to a paper towel-lined baking sheet. Serve falafels hot with side salad and drizzle with lemon tahini sauce.