Make the dough: whisk the flour, baking powder, and salt in a medium bowl. Add the yogurt and stir with a fork until crumbly.
Transfer to a work surface and knead with your hands, adding more flour as needed, until it forms a smooth ball. Divide into 4 balls; flatten slightly with the palm of your hand. Cover loosely with plastic wrap. Set aside.
Heat the grill to medium-high, direct heat (400 to 450°F).
Zest half the lemon into a large bowl and half into a smaller one. Slice the lemon in half and juice half into each bowl.
To the smaller bowl: add the feta, 1 tablespoon each of dill and mint, 1 tablespoon of the olive oil and several grinds black pepper. Smash with a fork until fully combined.
To the larger bowl: add the vinegar, remaining 1 tablespoon olive oil, a generous pinch of salt, and several grinds black pepper. Whisk to combine. Add the cucumber, onion, remaining 3 tablespoons dill and 1 tablespoon mint. Season with salt until it tastes really vibrant and flavorful.
Uncover the flatbreads and roll (with a floured rolling pin) into 6 to 8-inch rounds. Transfer to a rimmed baking sheet. Brush both sides with olive oil; place on the hot grill. Cover and grill until beginning to puff and the undersides are crisp, 2 to 4 minutes. Flip and grill until the second side is browned, 2 to 4 minutes more.
To grill the chickpeas: Heat a cast iron skillet directly on the grill grates until hot. Add a drizzle of vegetable or grapeseed oil. Once hot, add the chickpeas and cook until beginning to char and crisp. Season with salt to taste.
To assemble: spread the smashed feta onto the grilled flatbreads. Top with the salad, chickpeas, and a drizzle of tahini.
