Bake the Chickpeas. Preheat the oven to 350ºF. Remove the skins from the chickpeas, if desired. Add the olive oil, paprika, salt, and cayenne. Mix everything well and transfer it onto a baking sheet. Bake for 15 minutes.
Make Tzatziki. While the chickpeas are in the oven, make the sauce by mixing the tzatziki ingredients together in a small bowl.
Prep the Veggies. Slice the tomatoes, lettuce, cucumber, onions, and any other vegetables you are going to use.
Assemble the Gyro. Warm the pita bread (in the oven or microwave). Spread a generous amount of tzatziki and add the roasted chickpeas, feta cheese, and veggies on top. Fold the gyro* in half and serve.
*Follow my video instructions above in the "How To Fold a Gyro" section.