Preheat the oven on broil. Combine the anchovy, egg yolk, vinegar, lemon juice, olive oil, parmesan, salt/pepper to taste. Slowly drizzle the olive oil in to the mixture while whisking to form an emulsion.
Eric's way: Cut the romaine heart in quarters and place on the baking tray. Brush the dressing on the romaine hearts on the cut sides. My Way: Peel the individual lettuce wraps and place on baking sheet. Brush with caesar dressing.
Grate the parmesan cheese over the top. Season with salt the black pepper.
Place in the oven on broil for about 5 minutes or until the cheese is lighty brown. Be sure to closely monitor so you don't burn the lettuce! Place on large serving platter.
Pan sear the tomatoes in an iron cast over medium heat with 1 tablespoon of olive oil until charcoaled/blistering. Option to saute the chicken or leave cold. Layer on top of lettuce. Add avacado, salad topper, additional parmesan, and additional dressing. Serve immediately!