Heat a large skillet over medium heat. Add olive oil and let it warm up. Add diced onion and sauté for 3-4 minutes until translucent. Add minced garlic and cook for an additional minute until fragrant.
Increase heat to medium-high and add ground beef. Cook for 5-7 minutes, breaking it apart as it cooks. Stir in oregano, cumin, paprika, salt, and pepper. Cook for another 2-3 minutes, then remove from heat.
If desired, warm pita pockets in a toaster or skillet for about 1 minute.
Assemble the pita pockets by filling each with the beef mixture, fresh tomato-cucumber-feta salad, and drizzle with tzatziki sauce. Garnish with parsley and serve immediately.