Heat a large skillet over medium-high heat and add olive oil. Season chicken breasts with salt and pepper, then cook for 5-7 minutes on each side until golden brown and cooked through. Let rest, then smash into bite-sized pieces.
In a medium bowl, combine mayonnaise, lemon juice, Dijon mustard, minced garlic, and grated Parmesan cheese. Whisk until smooth and season with salt and pepper.
Warm tortillas in a dry skillet for 30 seconds on each side. Assemble tacos by adding smashed chicken, romaine lettuce, Caesar dressing, and additional Parmesan cheese.
Serve tacos on a platter with optional garnishes and extra dressing on the side.