The intense flavor of rosemary pairs well with the hearty taste of turkey. Add herbs to the pan after the turkey is seared to make a quick sauce.
One at a time, place turkey cutlets between two sheets plastic wrap. Using a meat mallet or heavy skillet, pound cutlets to a 1/4-inch thickness. In a large skillet, heat 1 tablespoon oil over medium-high. Season turkey with salt and pepper. In batches, cook turkey until cooked through, 1 to 2 minutes per side (add up to 1 tablespoon oil if needed, reducing heat to medium if skillet becomes too dark). Transfer turkey to a plate.
Add 1 tablespoon oil and shallots to skillet; season with salt and pepper. Cook, stirring occasionally, until shallots begin to soften, about 4 minutes. Add wine and rosemary and cook until syrupy, about 3 minutes. Add broth and cook until reduced by half, about 2 minutes. Return turkey to skillet and cook until warmed through, about 1 minute. Remove from heat and stir in butter; season with salt and pepper.