To make the dressing:
whisk the dijon mustard, egg yolk, anchovy paste, and garlic in a small bowl.
Whisk until homogeneous.
Slowly add the oil, whisky continuously, and making sure the oil gets fully incorporated.
Stir in the Parmesan and season with salt and pepper.
Refrigerate until ready to use.
Once you are ready to make the salads, turn on grill to medium-high heat.
Cut the romaine hearts in half, making sure to keep the layers of romaine together.
Brush each half (the inside of the romaine heart) with about a tablespoon of dressing, then place each romaine heart half (with the inside of the romaine down) on the grill and cook for 2-3 minutes.
Remove from heat and drizzle with more dressing.
Top with croutons, tomatoes, and additional Parmesan cheese.
Enjoy!