Place a large mixing bowl on a damp paper towel to prevent it from moving. Whisk together the shrimp paste (or anchovy paste), garlic, and egg yolks until smooth. Add the lemon juice, mustard and WS.
Pour the 1/2 cup of olive oil into the bowl in a slow, steady stream, whisking constantly to begin forming the emulsion. Add the vegetable oil in the same manner. Whisk constantly until your dressing leaves ribbon-like marks in itself.
Whisk in a 1/2 cup of parmesan cheese and season to taste with salt and pepper. Divide into two equal portions. Refrigerate one portion for later.
Toss the shrimp in the other portion to coat thoroughly. Allow the shrimp to marinate in the Cesar dressing for no more than 20 minutes.
Preheat your grill to medium heat (300°F).
Brush the romaine lettuce halves with the remaining olive oil and season with salt and pepper.
Drain the shrimp and grill, along with the lettuce (on the other side of the grill) for 7 minutes. Turn the shrimp once halfway through cooking. Don't turn the lettuce unless it begins to char too much. Remove both from the grill and allow to cool.
Chop the romaine into large pieces (about 1"). Toss with the remaining dressing and plate. Top with the shrimp, a sprinkling of parmesan cheese and croutons, if desired. Enjoy!