Preheat the grill to medium-high heat. Cut the lighter colored woodier ends of the asparagus and discard. Toss the asparagus with olive oil, salt, and pepper.
Grill for 4–6 minutes, turning occasionally, until lightly charred and tender-crisp. Transfer to a cutting board. Cut the asparagus stems into bite-sized pieces and reserve the tips for garnish.
Make the Caesar Salad Dressing
Whisk together the Greek yogurt, mayonnaise, lemon juice, Dijon mustard, garlic, parmesan, Worcestershire sauce, in a large salad bowl until smooth. Season with salt and pepper to taste.
Assemble the Grilled Asparagus Caesar Salad
Remove half of the dressing from the large bowl, into a smaller container and set aside.
When ready to serve, add the chopped romaine lettuce and the grilled asparagus stem pieces to the large bowl. Toss until evenly coated with the dressing.
Transfer the salad to a serving platter or bowl. Top with the reserved asparagus tips, shaved parmesan, and croutons. Serve immediately.