Soak the skewers in water for at least 30 minutes.
Season the cutlets evenly with the sage and lemon zest and then lightly season with salt and pepper.
Wrap each strip of cheese in a slice of prosciutto so the cheese is completely enclosed. Place one prosciutto-wrapped cheese strip on top of each turkey cutlet. Roll up the cutlets and secure them with skewers. Brush the turkey rolls all over with oil. Lightly season the outside of each turkey roll with salt and pepper. (The turkey rolls can be prepared to this point, up to 6 hours ahead, and kept covered in the refrigerator.)
Prepare the grill for direct cooking over medium heat (350° to 450°F).
Bring a large pot of salted water to a boil over high heat. Add the orzo and cook until just tender but still al dente, 8 to 9 minutes, stirring occasionally. Drain, rinse with cold water, and set aside. In a large skillet over medium-high heat, warm 2 tablespoons oil. Add the shallots and sauté until tender, about 4 minutes, stirring often. Stir in the sage, add 1 cup chicken broth and the peas, and bring to boil. Cook until the liquid is reduced by about one-third, about 2 minutes. Stir in the orzo, 1-½ tablespoons lemon juice, ½ teaspoon pepper, and ¼ teaspoon salt. Stir over medium heat until the orzo is coated with the mixture but still moist, 1 to 3 minutes. Add the cheese and stir to combine. The mixture should be moist, like risotto. If necessary, add more broth to achieve the right consistency, then add more lemon juice, salt, and pepper, if desired. Cover to keep warm.
Brush the cooking grates clean. Grill the turkey rolls over direct medium heat,with the lid closed as much as possible, until the meat is firm to the touch and no longer pink in the center, 4 to 6 minutes, turning occasionally. Remove from the grill and cut each turkey roll crosswise into slices. Serve warm with the orzo.
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