Preheat oven to 400 degrees. In a small bowl, mix rosemary, paprika, 1 1/2 teaspoons coarse salt, 1/2 teaspoon pepper, lime juice, and 4 teaspoons oil; rub all over turkey. Leaving space between them, place both halves in the center of a large rimmed baking sheet.
Brush cut sides of sweet potatoes with remaining 2 teaspoons oil; place, cut side down, on sheet with turkey. Roast until an instant-read thermometer inserted in the center of each breast half registers 160 degrees, about 50 minutes (potatoes should be tender). Let stand 10 minutes, loosely tented with aluminum foil to keep warm (temperature will rise by 5 degrees).
Cut one breast half into thick slices (reserve remaining turkey; see step 4). Cut potato halves into wedges. Transfer turkey slices and potatoes to a serving platter, drizzling turkey with any juices from baking sheet. (Optional: Serve with Sauteed Escarole.)
Cool remaining turkey completely. Divide leftovers evenly between two airtight containers, or wrap in plastic, and refrigerate.