2 hot green chiles (like Thai bird or serrano), cut into chunks, or to taste
4 garlic cloves, peeled and lightly crushed
6 tablespoons olive oil, plus more for greasing
2 tablespoons lemon juice
4 teaspoons ground cumin
1 1/2 teaspoons ground coriander
1/4 teaspoon ground cardamom
3cups flour, or more as needed
2 teaspoons instant yeast
2 teaspoons salt, or more as needed
1/2 teaspoon sugar
1 small onion, cut into chunks
1/2 teaspoon baking soda
1/4 teaspoon cayenne, or more to taste
Pepper
4 tablespoons unsalted butter, melted
Good-quality vegetable oil, for frying
Chopped romaine lettuce, tomatoes, cucumbers, and red onions, for serving
Instructions
Put the chickpeas in a large bowl and cover with water by at least 3 inches. Soak for 24 hours, checking once or twice to see if you need to add more water to keep the beans submerged.
Put 1 1/2 cups each of the cilantro and parsley in a food processor with the chiles, 2 garlic cloves, 3 tablespoons olive oil, 1 tablespoon lemon juice, 1 teaspoon cumin, 1/2 teaspoon coriander, and the cardamom. Process until smooth and pourable (add water 1 tablespoon at a time if the mixture is too thick). Taste and adjust the zhug. (The sauce is best after refrigerating at least a day and keeps for 5; to serve, bring to room temperature.)
Put the flour, remaining 3 tablespoons olive oil, the yeast, 2 teaspoons salt, and the sugar in a food processor. With the machine running, add 1 cup water through the feed tube. Process for about 30 seconds, adding more water, a little at a time, until the mixture forms a ball that is just slightly sticky to the touch. If it’s too dry, add another tablespoon of water and process for another 10 seconds. (In the unlikely event the mixture is too sticky, add flour, 1 tablespoon at a time.) Turn the dough out onto a floured work surface and knead by hand for a few seconds to form a smooth ball. Put the dough in a bowl and cover with plastic wrap; let it rise until the dough doubles in size, 1 to 2 hours. Clean the food processor.
Drain the beans thoroughly and transfer them to the food processor with the remaining 1/2 cup cilantro, 1/2 cup parsley, 2 garlic cloves, 3 teaspoons cumin, 1 teaspoon coriander, and 1 tablespoon lemon juice. Add the onion, baking soda, and cayenne. Season generously with salt and pepper and pulse until almost smooth, scraping down the sides of the work bowl if needed; add 1 or 2 tablespoons water if necessary to help the machine, but keep the mixture as dry as possible. It should hold together when you pinch some in the palm of your hand. Taste and adjust the seasoning. Transfer the mixture to a bowl and refrigerate until ready to fry.
When the pita dough is ready, divide it into 6 or 8 pieces and roll each into a ball. Put the dough balls on a lightly floured surface, not touching, and sprinkle with a little flour. Cover with plastic wrap or a towel and let rest until they rise a bit again, about 20 minutes.
Lightly flour your work surface and roll each ball out to rounds of about 1/8-inch thickness. As you work, put the rounds on a floured surface so they don’t touch and keep covered with a towel. Heat the oven to 350°F and let the dough rest for another 20 minutes. If you have a pizza stone, put it on a low rack in the oven; or, lightly oil a baking sheet and put it in the oven on a rack set in the middle.
To bake the pita on a stone, put the individual disks directly onto the stone without touching one another using a large spatula. Or put 2 disks at a time on the prepared baking sheet. Bake until the pitas are lightly browned on first side, then turn and brown on the other side, 2 to 3 minutes per side. As the pitas finish baking, remove them from the oven, brush with melted butter, and wrap in foil to keep warm.
Line a plate with paper towels. Put 2 inches of vegetable oil in a large pot over medium heat; bring to 350°F. Working in small batches to prevent crowding, scoop up heaping tablespoons of the falafel mixture and gently lower them into the hot fat, using another spoon to gently slide them in. Cook on all sides, flipping occasionally and adjusting the heat so the batter sizzles steadily without burning, until the falafel are brown and crisp, 3 to 5 minutes total. Drain on the paper towels and repeat with the remaining batter. Serve the falafel with the warm pita, passing the spicy zhug and any other fixings at the table.