In a medium bowl, stir together the mayo, mustard, lemon juice, garlic, and black pepper. Use a fork to mash the anchovies into the mixture and they will break apart and incorporate. Finally add in the parmesan and stir to combine. Cover and set aside in the fridge until ready to use.

Preheat grill to high and brush olive oil on the romaine. Sprinkle with salt. Place the romaine cut side down on the hot grill and cook about 3-5 minutes to char lightly but not wilt.

To serve, place the romaine charred side up on a plate, drizzle with the dressing and more cheese.