Soak beans overnight. Place beans in a large container and cover by 3 to 4 inches with water; they will triple in size. Let soak overnight, add more water if necessary.
Combine in food processor. Drain beans, saving the soaking water. Working in 2 batches, place half the beans in a food processor fitted with the blade attachment. Add half the parsley, garlic, onion, lemon juice, cumin, salt, coriander, pepper, baking soda, and cayenne.
Grind into falafel mixture. Pulse in 2 second pulses until all ingredients are minced and mixture comes together, but doesn't form a paste. Stop motor occasionally to scrape down sides of bowl and add reserved soaking water a tablespoon at a time if necessary to get a nice mixture that holds together easily when you squeeze a handful. Repeat with remaining falafel ingredients.
Shape and chill. Scoop into balls with a cookie scoop and leave as round balls or shape into 2-inch patties and set on a parchment-lined baking sheet. Place in the refrigerator for at least 30 minutes or up to overnight. If chilling overnight, cover loosely with plastic wrap. While falafel are chilling, make the tahini sauce and prep the salad ingredients.
Heat oil. Pour oil in a large cast iron skillet or frying pan until it reaches an inch up the sides of the pan. Heat oil over medium heat until it reaches 350°F on a deep fat fry thermometer or until a wooden chopstick inserted in the oil is immediately covered with bubbles. This can take up to 5 minutes to heat.
Fry. Add patties a few at a time and let fry until browned on one side, about 2 to 3 minutes. Flip and repeat on the other side. (If they are browning too quickly reduce heat or raise the heat if not fast enough.) Remove from oil to a paper towel-lined baking sheet and sprinkle with salt. Repeat with remaining patties.
Enjoy! Continue with instructions to make the salad. You can also serve the falafel on their own with the tahini sauce as an appetizer or make into a sandwich by tucking them into a toasted pita or lavash with some lettuce, cucumbers and olives and a drizzle of sauce on top.