Preheat grill or grill pan to medium-high.
In the bowl of a food processor, combine the avocado, lemon juice, anchovy paste, garlic, Worcestershire, cheese, salt and lots of pepper. Pulse the machine to chop everything up then leave it on and stream about 1/4 cup EVOO into the mixture until a thick dressing forms. Reserve.
Pat the romaine hearts dry, spray the cut sides and grill, cut side-down, until marked, about 2 minutes. Serve the grilled romaine topped with the Caesar-cado dressing. Serve alongside Tequila-Lime Chicken with Tex-Mex Chimi-Chop.