Step 1

Combine the olives, cucumbers, red pepper and onion in a mixing bowl. Add the lemon juice, olive oil, a big pinch of salt and some black pepper and toss to combine. Allow to marinate in the refrigerator while you make the feta.

Step 2

For the feta, prepare a dredging station. In a rimmed dish, add the flour. In a separate rimmed dish, whisk the egg with a splash of water. In a third separate dish, whisk together the breadcrumbs, 1/2 teaspoon salt and a few turns of black pepper. Coat each chunk of feta in the flour and tap off the excess. Dunk in the beaten egg and then coat in the breadcrumbs, tapping off the excess.

Step 3

Heat a 1/4-inch layer of olive oil in a 10-inch nonstick skillet over medium heat. (Test to see if it is hot enough by sprinkling a bit of breadcrumb in the oil. If it sizzles right away, it’s ready.) Carefully place the breaded feta cubes in the oil and fry in batches for 90 seconds to 2 minutes on the first side, undisturbed. Flip and fry on the other side for another minute or so, or until golden brown. Remove to a cooling rack set over a baking sheet and allow excess oil to drain. Repeat until all pieces are fried.

Step 4

To serve, slice open each pita and create a pocket. Schmear a big plop of hummus inside each one, followed by some arugula. Top with a pile of the Greek salad, a few chunks of the warm, fried feta, a dollop of yogurt and a few pieces of mint. Serve with lemon wedges and hot sauce, if desired.

Step 5

In the bowl of a stand mixer fitted with a dough hook, mix together the water, sugar and yeast just to dissolve. Add the oil and salt and then gradually add the flour. Increase the speed to medium-high and mix for 7 to 10 minutes, adding just enough additional flour so that the dough no longer sticks to the bowl. Do not add too much flour. The dough should be smooth and slightly sticky. Lightly coat a clean large bowl with oil or cooking spray, then place the dough in the bowl and turn it once or twice to coat it in oil. Cover the bowl with plastic wrap and let it rise at room temperature for 2 hours, or until it has doubled in size.

Step 6

Turn the dough onto a clean work surface and divide it into 8 equal pieces. Mold each piece into a ball by stretching the top and tucking the edges under. Place the balls 1 inch apart on a piece of parchment paper, cover them with plastic wrap and let them rise for 30 minutes.

Step 7

Set an oven rack in the middle position. Preheat the oven to 500 degrees F. Line 2 baking sheets with parchment.

Step 8

With a rolling pin, roll out the balls of dough into 6-inch circles. Place them on the baking sheets and bake for about 5 minutes, or until they're puffy and just starting to brown.