Mix the Anchovy and Garlic: Finely mince garlic clove on a cutting board, or use a garlic press. Add anchovy paste and salt. Smash the mixture with the sides of a knife until a paste forms.
2-3 tsp. anchovy paste, 1 large clove garlic, ¼-½ tsp. salt
Make the Base: Place a towel in a medium-sized saucepan and then add a medium-sized bowl. (This helps to stabilize the bowl while you’re using both hands! This is NOT done on the stovetop.) Add the egg yolk, lemon juice, and mustard. Whisk vigorously until it begins to get frothy and bubbles form on top of the surface.
2 Tbsp. lemon juice, 1 large egg yolk, 1 tsp. Dijon mustard
Emulsify with Oil: Drip in 1-2 tablespoons of oil, drop by drop, while continuing to whisk. Wait for it to thicken up and then slowly pour in the remaining oil, one tablespoon at a time. When done slowly you'll create an emulsion of ingredients.
½ cup oil
Bring it All Together: Mix in the anchovy mixture, Parmesan cheese, and black pepper. If the mixture is too thick, slowly add in water until your desired consistency is reached. Serve Caesar salad dressing immediately or store in the refrigerator for up to a week.
¼ cup Parmesan cheese, ⅛ tsp. black pepper, 1-2 Tbsp. water