Make your chicken marinade. Add 2 tablespoons of Greek yogurt, the crushed garlic, 2 tablespoons of lemon juice, 1 tablespoon white wine vinegar, 1 tablespoon olive oil, 2 tablespoons of dried oregano, 1 teaspoon of salt, 1 teaspoon of smoked paprika, and 1 teaspoon of ground cumin to a large bowl. Mix well to combine.
Marinate your chicken. Add the chicken thighs, then toss them through the marinade really well so every piece is coated. Set aside while you prep the pita chips, or cover and marinate in the fridge for up to 24 hours.
Prep the pita chips. Cut your pita pockets or flatbreads into small triangles. If you're using pita pockets, I like to open up the pockets (so you're left with two thinner pieces) before slicing them into chips. Otherwise, I find they can be quite thick. Add them to a large bowl with 2 tablespoons of olive oil, 2 tablespoons of za'atar, and 1 teaspoon of sumac. Toss very well so they're evenly coated. PRO TIP: I sometimes find this easier to do in two batches - it can make it easier to make sure the chips are seasoned evenly.
Make the crispy chickpeas (optional). Drain your chickpeas, then rinse them in a colander. Add them to a bowl with 1 tablespoon of olive oil, ½ teaspoon of salt, and 2 teaspoons of smoked paprika. Toss to combine, then transfer them to your air fryer basket. Air fry at 400°F (200°C) for 15 minutes, giving the basket a shake halfway through the cooking time.
Cook the pita chips. Transfer the pita chips to your air fryer basket (you may need to do this in batches depending on the size of your air fryer). Try not to pile them up too much - a little overlap is ok - but you don't want them all stacked on top of each other, or they won't cook evenly. Air fry at 350°F (180°C) for 8 minutes, giving the basket a shake halfway through, until golden and crispy. You may need to cook your chips longer if your flatbreads are thicker, or if you don't split your pita.
Cook the chicken. Add the marinated chicken to your air fryer basket in a single layer. Air fry at 400°F (200°C) for 12 minutes, until gorgeously golden and lightly charred around the edges. If you have a probe thermometer, check that the chicken has reached an internal temperature of 165°F (74°C). Transfer it to a board and leave it to rest for about five minutes before thinly slicing or shredding it.
Make the garlic tahini sauce. Add ½ cup of tahini, 1 tablespoon of lemon juice, ½ teaspoon of salt, and the crushed garlic to a small bowl. Use a fork to mix - it will thicken and look quite split and grainy at first, but trust the process! Add cold water, 1 tablespoon at a time, mixing as you go, until the sauce is super smooth, creamy, and a bit like the consistency of heavy cream. Taste and add a little more lemon juice or salt if needed. PRO TIP: The sauce will thicken as it sits, but you can easily loosen it again by mixing in a little more water.
Make the salad. Add the chopped tomatoes, cucumber, olives, feta, flat-leaf parsley, 1 teaspoon of sumac, and a good grind of black pepper to a bowl. Toss to combine. PRO TIP: I'm purposely not adding extra salt here as the olives and feta are salty, and the sumac helps brighten the flavors, but you can add a little pinch of salt if you like.
Assemble the nachos. Arrange the crispy pita chips on a large serving platter. Spoon over the juicy shredded chicken, then scatter over the salad. Drizzle with most of the garlic tahini sauce, then sprinkle with crispy chickpeas (if you've made them), a little more chopped flat-leaf parsley, extra za'atar, and sumac if you like.