Thinly slice the chicken breasts lengthwise to make thin chicken cutlets. Season the chicken all over with salt and pepper. Line a baking sheet with paper towels.

Place the eggs in a shallow plate or bowl. Stir together the breadcrumbs and parmesan in another plate or bowl.

Heat 1 to 2 tablespoons of olive oil in a large skillet over medium heat.

Dip each piece of chicken into the egg, then into the breadcrumbs, pressing gently so the crumbs adhere.

Add the chicken 2 to 3 pieces at a time. Cook on each side until deeply golden, about 3 to 4 minutes per side. Remove each piece of chicken and place it on the paper towel-lined sheet. Repeat with remaining chicken.

To make the dressing, add the garlic, yogurt, parmesan, mustard, vinegar, anchovy paste, lemon juice, salt, and pepper to a food processor or blender and blend until pureed. Stream in the olive oil until a creamy dressing forms.

Place the romaine in a large bowl and toss with a big pinch of salt and pepper. Drizzle with a few tablespoons of the caesar dressing. Add in the finely grated and shaved parmesan. Toss well to coat the lettuce.

Assemble the sandwiches by placing a cutlet (or 2) on a bun and topping it high with caesar salad.