Lightly brush rolls with 2 tablespoons of the butter. Heat large skillet on medium heat. Place rolls, buttered-side down, in skillet. Toast 2 to 3 minutes per side or until golden brown. Remove from skillet. Set aside.
Heat oil and remaining 1 tablespoon butter same skillet on medium heat. Add shallots and garlic; cook and stir 1 minute or until fragrant. Add shrimp, paprika, salt and pepper; cook and stir 3 to 4 minutes or just until shrimp turn pink. Stir in sherry and vanilla; cook until heated through.
Spread mayonnaise on each roll. Place baby greens in rolls. Spoon shrimp mixture into each roll. Drizzle shrimp with remaining sauce. Serve immediately.