Pulse chickpeas in a food processor, scraping down sides as needed, until they resemble finely chopped nuts (the texture should be uneven, with some slightly larger pieces visible), about 1 minute. Transfer to a large bowl.
Pulse onion, jalapeño, garlic, cilantro, and parsley in food processor, scraping down sides as needed, until coarsely chopped, about 1 minute. Mix into chickpeas, then mix in chickpea flour, salt, baking powder, cardamom, and cumin. Form into ping-pong–size balls.
Pour oil into a large heavy pot to a depth of 3". Fit pot with thermometer and heat oil over medium-high until thermometer registers 330°. Working in batches, cook falafel, turning occasionally, until deep brown and crisp, about 5 minutes. Transfer to paper towels; let sit 5 minutes.
Serve falafel in pita with cabbage, tomato, and tahini. Enjoy!