Spray a large skillet with nonstick cooking spray over medium heat.
In a large bowl, combine the ground turkey, basil, garlic, salt and pepper. Add the mayonnaise, stirring to combine. Shape the mixture into eighteen 2-inch-size patties.
When the skillet is hot, add the turkey sliders in batches, and cook until done all the way through, 4 to 5 minutes per side. Spread desired amount of Roasted Red Pepper Mayonnaise onto the buns. Top the bottom halves of the buns with desired amount of shredded lettuce. Top each with 1 turkey slider. Cover with the top halves of the buns. Serve immediately.
In a small bowl, combine the mayonnaise, mustard and garlic. Stir in the peppers and season with salt and pepper. Cover and chill.