Season chicken breasts with olive oil, garlic powder, salt, and pepper.
Grill or pan-sear chicken over medium-high heat for 6-7 minutes per side until cooked through (internal temp 165°F). Let rest 5 minutes, then slice thinly.
While chicken rests, make dressing: whisk together mayonnaise, lemon juice, Dijon mustard, Worcestershire sauce, grated Parmesan, and minced garlic. Season with salt and pepper. Add anchovy paste if using.
Toast bread slices or rolls until golden.
In a large bowl, toss chopped romaine with a few tablespoons of dressing—just enough to coat lightly.
Assemble sandwiches: spread a little extra dressing on bottom bread, pile on dressed romaine, add sliced chicken, and top with shaved Parmesan. Close with top bread and press gently. Serve immediately or wrap tightly for later.