Prepare the Turkey Breast: If the turkey breast is tied, remove any ties and pat the meat dry with paper towels. Chop enough rosemary leaves to measure about 1 tablespoon, keeping the rest of the sprigs intact for later use.
Make the Marinade: Using a mortar and pestle or the back of a spoon in a bowl, crush together the chopped rosemary, garlic, anchovies, lime zest, kosher salt, and black pepper until it forms a coarse paste. Stir in the olive oil to create a smooth mixture.
Apply and Marinate: Spread the rosemary-anchovy paste evenly over the turkey breast, ensuring it is well-coated. Place the turkey in a bowl, cover it loosely with plastic wrap, and let it marinate at room temperature for at least 30 minutes. For a deeper flavor, refrigerate it for up to 24 hours.
Preheat the Oven: Set your oven to 400°F and allow it to preheat while you prepare the turkey for roasting.
Assemble for Roasting: Arrange the remaining rosemary sprigs on the bottom of a roasting pan or a rimmed baking sheet. Roll the turkey breast into a compact shape if necessary and secure it with kitchen twine to maintain its form. Place the turkey breast skin-side up on top of the rosemary sprigs.
Begin Roasting: Roast the turkey breast at 400°F for 25 minutes to develop a flavorful crust. Then, reduce the oven temperature to 350°F and continue roasting until a meat thermometer inserted into the thickest part of the turkey reads 145°F. This should take an additional 20 to 30 minutes.
Rest and Slice: Remove the turkey from the oven and let it rest for 10 minutes to allow the juices to redistribute. Untie the turkey if twine was used, and then slice it for serving.