In a medium-sized mixing bowl, whisk together all the ingredients for the dressing until smooth and well combined. Cover and refrigerate while you prepare the salad, to allow the flavors to meld.
Pat the shrimp dry with paper towels.
In a large mixing bowl, toss the shrimp with 1 tablespoon olive oil, lemon juice, and Old Bay Seasoning until evenly coated.
Heat the remaining two tablespoons of olive oil in a large skillet over medium-high heat. Add the shrimp in a layer and cook for 2-3 minutes per side. The shrimp should be pink, opaque, and lightly browned. Remove from heat and set aside to cool slightly.
In a large serving bowl, add the chopped romaine lettuce, croutons, and shaved parmesan cheese. Drizzle with ½ cup of the prepared Caesar dressing and toss gently to coat.
Top with the cooled shrimp, then finish with additional Parmesan and freshly cracked black pepper, if desired. Serve immediately.