Place the chickpeas on a baking sheet, in an even layer, and pat dry very well with a few paper towels or a clean kitchen towel. Transfer to a food processor and pulse a few times until coarsely ground. You don't want to process them too much. Transfer to a large bowl and set aside.
Place the onion, jalapeño, garlic, cilantro and parsley in the food processor and pulse until coarsely chopped as well. Transfer to the bowl with the chickpeas. Add the chickpea flour, egg, salt, baking powder, cardamom, and cumin and stir until evenly combined. Divide the mixture into four equal portions and form each, packing tightly, into patties. Place on a baking sheet lined with parchment or wax paper and chill for at least 1 hour to firm up.
Meanwhile, to make the sauce, combine the yogurt, garlic, lemon juice, cucumber, herbs, crushed pepper flakes and a pinch of salt and pepper in a bowl and stir until well combined. Stir in the feta and chill until ready to use.
Preheat oven to 200°F. Place a wire rack over a baking sheet and set aside.
Fill a large skillet, with high sides, with about 2-inches of oil and place over medium-high heat until hot. Carefully lower a falafel patty into the hot oil and fry for about 2 to 3 minutes per side until golden brown and crispy all around. Transfer to the prepared wire rack and sprinkle with salt while hot. Keep warm in oven while you fry the rest.
To assemble the burgers, spread both the top and bottom halves of the toasted buns with the tzatziki sauce. Place a falafel patty on top of the bottom bun and top with onion, tomato and lettuce. Place the top bun on and skewer with a long toothpick. Serve immediately and enjoy!