Peel and devein the shrimp, leaving the tails on. Place them on a sheet pan with the olive oil, salt, and pepper and spread them in one layer. Roast for 8 to 10 minutes, just until pink and firm and cooked through. Set aside to cool.
For the dressing, place the mayonnaise, scallions, basil, lemon juice, garlic, anchovy paste, salt, and pepper in a blender and blend until smooth. Add the sour cream and process just until blended. Use immediately or refrigerate until ready to use. Serve as a dip for the shrimp with the celery sticks.