In a small bowl, whisk together Greek yogurt, mayonnaise, grated Parmesan, lemon juice, Dijon mustard, Worcestershire sauce, minced anchovy, and grated garlic until smooth and creamy. Taste and season with salt and pepper. Set aside.
Melt butter in a skillet over medium heat. Add panko breadcrumbs and toast, stirring constantly, for 1-2 minutes until golden brown and nutty. Immediately transfer to a small bowl and season with salt. Wipe the skillet clean.
In a large bowl, combine ground chicken with Italian seasoning, garlic powder, onion powder, smoked paprika, salt, and pepper. Mix until just combined. Divide into 8 equal portions (about 2 ounces each) and roll into loose balls.
Place one ball of seasoned chicken in the center of each tortilla. Gently press and spread toward the edges, leaving about a 1/2-inch border. The chicken layer should be roughly 1/4 inch thick across the entire surface.
Heat avocado oil in a large skillet over medium-high heat until shimmering. Working in batches of 2-3, place tacos chicken-side down in the skillet and press firmly for 20-30 seconds. Cook for 2-3 minutes until golden and crisp. Brush tortilla tops with oil and sprinkle with mozzarella. Flip and cook for 1 more minute until tortilla is browned and cheese is melted.
While tacos cook, toss the finely chopped romaine with about half of the prepared Caesar dressing until lightly coated. Keep cold until ready to assemble.
Place finished tacos on a serving platter with the crispy cheese side facing up. Top with a generous handful of dressed romaine, drizzle with extra Caesar dressing, scatter with toasted panko breadcrumbs, and finish with freshly grated Parmesan. Serve immediately.