Combine olive oil, red wine vinegar, minced garlic, dried oregano, salt, and pepper in a baking dish. Add the steak and marinate for 15 to 30 minutes to infuse the steak with flavor.
Meanwhile, heat the grill to medium-high heat.
Toss the sliced veggies in olive oil and sprinkle with salt, pepper, and dried oregano.
Place a sheet of foil on the grill and add the veggies. Grill for 15 to 20 minutes, flipping occasionally until seared and slightly charred.
Prepare the lemon herb Greek Yogurt Sauce
In a small bowl, combine the yogurt, minced garlic, lemon juice, dill and mint, salt, and pepper and stir well to combine.
Add the steak to the grill and cook for 4-5 minutes on each side until cooked through. The grilling time will vary depending on the thickness of your steak. Be sure to use a thermometer to check the internal temperature.
Since a petite sirloin is very thin - it cooks incredibly fast, so plan on 8-10 minutes total grilling time for that cut of beef.
While the steak is grilling, prepare the naan. In a small bowl, pour olive oil and add a pinch of salt, pepper, dried oregano, or you can use your favorite all-purpose spice blend - like Kinders or Grill Mates Montreal Seasoning blend.
Lightly brush the seasoned olive oil over the naan.
Once the steak is cooked, remove it from the grill, cover to rest for a few minutes, then thinly slice the steak against the grain.
Add the naan to the grill to toast both sides - about 2-3 minutes per side.
Remove the grilled veggies to a plate and assemble the gyros.
Assemble the gyros by layering the lemon herb Greek yogurt sauce over the toasted naan, then the sliced steak, grilled veggies, a handful of arugula and feta cheese.
Notes
The naan is larger than pita bread, so it's difficult to fold like traditional gyros - but you can cut it in half to roll, or cut into quarters to eat as a flatbread.