Whisk flour, 1/4 teaspoon salt and pepper in a shallow dish. Dredge each turkey cutlet (or steak) in the flour mixture. Heat 1 tablespoon oil in a large nonstick skillet over medium-high heat. Add the turkey and cook until lightly golden, 2 to 3 minutes per side. Transfer to a plate; cover with foil to keep warm.

Add the remaining 1 tablespoon oil to the pan and heat over medium-high heat. Add mushrooms and onion (or scallion) whites and cook, stirring often, until the mushrooms are browned and the whites are slightly softened, 2 to 3 minutes. Add broth, wine and the remaining 1/4 teaspoon salt; cook, stirring occasionally, until the sauce is slightly reduced, 2 to 3 minutes. Stir in peas and onion (or scallion) greens and cook, stirring, until heated through, about 1 minute. Stir in lemon zest. Nestle the turkey into the vegetables along with any accumulated juices from the plate. Cook, turning the cutlets once, until heated through, 1 to 2 minutes.