How to Make It
Preheat oven to 375°F. Line a rimmed baking sheet with parchment paper. Set aside.
Remove beans from pod. Prepare a large bowl of ice water fitted with a colander. Bring a large saucepan of water to a boil over medium-high. Add beans and cook until just tender, about 2 minutes. Drain; transfer to colander. Peel beans (pierce skins with a paring knife; squeeze to pop out beans). Discard skins.
Add ¾ cup fava beans to the bowl of a food processor and pulse until roughly chopped, 3 to 4 times. Transfer to a large bowl. Add garlic, cilantro, lemon zest, cumin, coriander, flour, baking powder, ½ cup of the parsley, half of the shallot, 1¼ teaspoons of the salt, ¼ teaspoon of the pepper, and remaining 2 cups fava beans. Process until a coarse paste forms, about 30 seconds. Transfer to bowl with chopped favas and mix to combine. Form into 20 balls (about 1 heaping tablespoon each).
Heat oil in a large nonstick skillet over medium. Add falafel and cook, turning with tongs, until crispy, about 5 minutes. Transfer to prepared baking sheet and bake in preheated oven until dry to the touch, 14 to 16 minutes.
Combine tomatoes, cucumbers, ¼ cup of the parsley, ¼ teaspoon of the salt, ⅛ teaspoon of the pepper, and remaining shallot in a large bowl.
Chop remaining 1 tablespoon parsley; transfer to a small bowl. Add the yogurt, lemon juice, remaining ¼ teaspoon salt and ⅛ teaspoon pepper; stir to combine.
Split pitas and stuff with tomato-cucumber salad and falafel. Drizzle with yogurt sauce. Serve with remaining salad and yogurt.