Preheat your oven to 350 degrees Fahrenheit
Cut each of the pita breads into 8 triangular pieces. The easiest way to do this is to cut them in half down the middle and then cut each half into four wedges.
In a large bowl whisk together the olive oil, mizithra, oregano, paprika, salt and pepper. Add the pita wedges to this bowl and use your hands to mix everything together very well. It is helpful to use your fingers to rub the oil mixture into the pita bread.
Place your pita wedges onto 2 baking trays trying not to have too much overlap. Bake in the middle rack of your oven for 5 minutes. Flip your pita over and continue baking for an additional 5 minutes or so. Your pita wedges should be crisp and slightly browned, but not burnt. Set them aside to cool.
Begin to prepare the toppings for your nachos. First you will seed and chop your tomatoes. We have found that the easiest way to seed your tomatoes is to cut them in rounds, width-wise and to remove the seeds with a small spoon. Then, you can chop your tomato into bite size pieces. You can see how we do this by clicking on this video.
Combine the tomatoes, cucumbers, red onion, oregano, salt, olive oil, balsamic vinegar and chopped parsley in a bowl. Mix well and let sit for at least 5 minutes.
Now it is time to assemble your nachos. Place half of your pita chips on a large serving platter. On top of this place half of your tomato mixture, half of your sliced radishes, half your crumbled feta and half your pitted Kalamata olives. Top this with the remaining pita chips and then add the rest of your toppings. Sprinkle with the chopped green onion.