To make the marinated tomatoes, toss garlic, thyme, mint, red pepper flakes, coriander, cumin, salt, and tomatoes in a bowl. Let sit at room temperature for 30 minutes.

To make the chickpeas, add chickpeas and vinegar to a bowl. Season with salt and pepper. Mash half with a fork until about half of the chickpeas are smashed. Add shallots, parsley, and olive oil. Set aside.

To make the yogurt sauce, mix everything together in a small bowl. Check for seasoning, and let sit for 15 minutes at room temperature.

To make the flatbread, whisk baking powder, sugar, flour, and salt in a large bowl. Add the yogurt and stir to combine. Transfer the dough to a floured work surface and knead until smooth, about 1 minute. Divide into 4 pieces, clover with a towel, and let rest for 15 minutes.

Working with one flatbread at a time, roll out dough to 1/8" thick. Heat one tablespoon of oil in a large skillet (cast iron works well) over medium heat. Add dough to hot pan and cook until underside is golden brown, about 2 minutes. Flip, and cook for an additional minute. Transfer to a plate. Repeat until all the dough is cooked.

To assemble the flatbreads, top flatbreads with yogurt sauce, tomatoes, and chickpeas. Top with crumbled feta cheese and more mint.