Prep the romaine: Rinse, dry very well, and chill in the fridge. Cold lettuce holds dressing better and stays crisp.
Make the dressing: In a bowl, whisk mayonnaise, Dijon, lemon juice, Worcestershire, anchovy, and grated garlic.
Stream in olive oil while whisking. Stir in Parmesan. Season with pepper and a pinch of salt.
Taste and adjust lemon or anchovy to your liking.
Season the shrimp: Pat dry. Toss with 2 tablespoons olive oil, minced garlic, 1/2 teaspoon salt, and several grinds of pepper.
Sear the shrimp: Heat a large skillet over medium-high. Add shrimp in a single layer.
Cook 1–2 minutes per side until pink and opaque with a slight golden edge. Do not overcook. Transfer to a plate and let rest 1–2 minutes.
Toss the greens: In a big bowl, add romaine, half the croutons, and half the Parmesan.
Drizzle on enough dressing to lightly coat. Toss gently with clean hands or tongs until glossy.
Assemble: Top with warm shrimp, remaining croutons, and more Parmesan. Add a squeeze of lemon if you like extra brightness.
Serve right away: Caesar is best when the lettuce is crisp and the shrimp are warm.