Add the Greek yogurt, Kewpie mayo, tahini, lemon juice, grated garlic, Worcestershire sauce, freshly grated Parmigiano Reggiano, anchovy paste, and Dijon mustard to a medium bowl. Whisk until completely smooth and creamy with no visible lumps. Taste and adjust lemon, salt, and anchovy paste as needed. The dressing should be bold, tangy, and well seasoned on its own. Set aside to rest while you prepare everything else.

If using homemade frozen falafel, place in the air fryer at 375F for 6 minutes until crispy and warmed through. If using Trader Joe's frozen falafel follow the package instructions. Both come out perfectly crispy from the air fryer.

Lay one large burrito tortilla flat on a clean surface. Spoon a generous dollop of Caesar dressing in the center of the tortilla. Layer the chicken strips in the center followed by the dressed romaine and then 2 falafel. Place one small 6 inch tortilla directly on top of the filling stack.

Fold the edges of the large tortilla up and over the small tortilla one section at a time, pleating as you go to create a sealed parcel. Press firmly with your hands to hold the folds in place. Repeat with the remaining 3 crunchwraps.

Heat a drizzle of olive oil in a large skillet over medium heat. Place the crunchwrap seam side down in the pan and press gently with a spatula so the entire surface makes contact. Cook for 2 to 3 minutes without moving until the underside is deeply golden and the seam is sealed. Flip carefully and cook for another 2 minutes until the second side is equally golden.

Remove from the pan and slice in half with a sharp knife. Serve immediately while the outside is still crispy and the inside is warm. Serve the remaining Caesar dressing alongside for dipping.