Preheat the oven to 400°F. Line a large sheet pan with parchment paper and set aside a second sheet of parchment for rolling.
Mix the ground chicken: Grate the onion using a box grater or blend it in a small food processor until finely broken down. Transfer to a large bowl and add the grated garlic, ground chicken, Greek yogurt, oregano, kosher salt, onion powder, red pepper flakes, and parsley. Mix with a rubber spatula or clean hands until fully combined.
1/2 medium onion, 3 cloves garlic, 1 lb ground chicken, 3 tablespoons plain Greek yogurt, 1 teaspoon dried oregano, 1 teaspoon kosher salt, 1 teaspoon onion powder, Pinch of red pepper flakes, 2 tablespoons fresh parsley
Press the chicken flat: Divide the meat mixture in half. Place one portion in the center of a large sheet of parchment paper and press it down firmly into a very thin layer. I like to spray a separate piece of parchment paper with nonstick spray, place it on top and roll it out with a rolling pin then peel off the top parchment.
Roll with parchment paper: Fold the bottom edge of the parchment up over the meat, then roll the meat forward in 2-inch increments, pressing gently as you go, until the log is fully wrapped. Transfer to the prepared sheet pan. Repeat with the remaining meat and another sheet of parchment.
Add vegetables: Arrange the halved tomatoes, quartered zucchini, and red onion chunks around the meat on the sheet pan. Drizzle the vegetables with olive oil and season with salt and pepper.
2 roma tomatoes, 2 medium zucchini, 1/2 red onion, 1 tablespoon olive oil, Salt and pepper to taste
Bake and tear: Bake for 20 minutes, until the meat is cooked through and the vegetables are tender. There will be some moisture from the chicken on the pan (this is ok). Carefully use tongs to unroll the chicken then use two forks or your hands to tear the chicken into long strips and place them back on the pan. It will likely absorb some of the released moisture.
Broil: Switch the oven to broil on high. Return the pan back to the oven and broil for 3 to 5 minutes, watching closely, until the tops are golden and the edges are slightly crispy. If using pita, add it to the lowest rack of the oven to warm.
Serve: Let the meat rest for 5 minutes, then slice into rounds. Serve in warm pita or over rice with hummus, tzatziki, feta, pickled red onion, shredded lettuce, and any other toppings you like.