Preheat oven to 450°F and arrange a rack in the center of the oven.
Add potatoes to a medium saucepan and cover with 2 inches cold water. Salt the water heavily. Bring to a boil and cook potatoes until the larger potatoes have no resistance when pricked with a knife, 20-25 minutes (depending on the size of your potatoes). Drain.
Once potatoes are cool enough to handle (but still warm), use the bottom of a measuring cup and gently press down to smash. Arrange smashed potatoes on a rimming baking sheet and drizzle with 1/4 cup olive oil. Flip potatoes and move them around so they are oiled on both sides. Bake until golden brown, 25-30 minutes, flipping with a rubber or fish spatula half way through.
Meanwhile, make the dressing. In a medium bowl, whisk yolks until smooth. Add mustard, anchovies, garlic, lemon juice and zest. Pouring slowly, add 2 tablespoons extra virgin olive oil while whisking constantly so that the mixture emulsifies. Add remaining 1/4 cup oil and continue to whisk while the dressing thickens. Whisk in grated Parmesan and season with salt and black pepper, to taste. If dressing is really thick, thin with a little water.
Add lettuce to a medium mixing bowl and toss with half of the Caesar dressing. Season with salt and pepper, to taste.
Once potatoes are done, drizzle them with remaining 1/2 of caesar dressing and top with dressed Romaine. Serve with more Parm and black pepper immediately.