Soak dried chickpeas and broad beans overnight in three times the amount of water to beans, allowing them to rehydrate and double in size. The next day, drain and rinse the beans, then let them sit in a colander while you peel the broad beans, discarding the skins.
In a high-speed food processor, add the beans and process until roughly chopped, about one minute. Add the remaining ingredients and process in one-minute intervals, scraping down the sides and mixing thoroughly to ensure an even texture. Repeat this process 5 to 6 times until the mixture has a fine, grainy, and moist consistency.
Transfer the mixture to a bowl and knead it with your hands for about a minute, ensuring everything is evenly mixed and checking for any large pieces. If there are, blend again until even. Cover and let the mixture rest in the fridge for at least 30 minutes.
Heat frying oil in a saucepan to a depth of at least 2 inches (5 cm) over high heat. Once the oil is hot, pack the mixture into a falafel maker, shaping it into a domed puck just over an inch thick. I recommend watching my "how to shape falafel" video for a visual guide.
Gently place the shaped falafel into the hot oil and fry until reddish, about 2 to 2½ minutes, turning occasionally with a slotted spoon. Remove the falafel with the spoon and place it on a paper towel-lined plate. You can fry several falafel at a time, but do not overcrowd the oil to prevent the temperature from dropping and causing the falafel to fall apart. Serve immediately and enjoy! I've listed some serving suggestions below.
