Preheat your oven to 400 degrees. To begin your salad, cube and toast your croutons with olive oil, salt and pepper until golden brown. Remove from oven and let cool.
Begin to shred your romaine and Brussel sprouts. Set aside.
Make your dressing by mixing olive oil, anchovy oil, garlic cloves, mayo, lemon, dijon, Worcestershire, shredded parmesan and salt and pepper in a bowl until the olive oil is set with the rest of the ingredients.
Begin to assemble your salad by placing your Brussels sprouts and romaine in a big bowl, add your cooled croutons, more parmesan, salt, pepper and then your dressing. Mix well and serve!