Preheat oven to 350F. Line a small baking pan with parchment paper.
In a food processor, combine the red onion, garlic, basil, and mint. Pulse until really fine texture. Transfer to a large bowl.
Add the ground beef, flour, egg, and spices to the bowl. Mix just until well-combined.
Form into long, thin patties.
Place a skillet over medium heat. Add the olive oil to heat up for 1 minute.
Sear the beef koftas for 2-3 minutes on each side, until crisp and browned. Transfer to the prepared pan to finish cooking in the oven for 6-8 minutes, depending on how thick they are. They may not need to be transferred into the oven if they're thin enough to finish cooking on the stovetop.
To assemble the wrap, layer the lavash bread with baby arugula, tzatziki, 2-3 beef koftas, sprouts, pickled onions, and cherry tomatoes. Enjoy!