In a large bowl with a lid, whisk together the yogurt, 2 tablespoons olive oil, lemon zest and juice, honey, oregano, paprika, garlic, 1 ½ teaspoons salt and ½ teaspoon pepper until smooth. Add the beef to the bowl and use your hands to mix and rub everything together. Let marinate for at least 45 minutes or up to 2 hours (see note).
Heat your grill up on high at least 15 minutes before you want to start grilling.
In a small bowl, make your tzatziki by mixing all ingredients together until smooth. Taste and add more salt or lemon, if needed.
Add veggies to a medium bowl and toss with remaining 1 tablespoon oil, ½ teaspoon salt, and ½ teaspoon pepper.
Form your kebabs by alternating between marinated beef and veggies. Grill the kebabs until cooked through and charred, about 10 minutes, rotating them halfway through.
Warm your pitas up on the grill. Fill them with the beef kebab contents and top with tzatziki sauce and parsley (if using).