Sprinkle cutlets with salt and freshly ground black pepper. Sprinkle cutlets with flour, shaking off any excess. Heat 2 tbsp evoo in heavy large skillet over medium-high heat. Add cutlets to skillet and sauté until cooked through and golden brown, about 3 minutes per side. Add a little more evoo if the pan starts to look dry when you flip the cutlets. Transfer turkey to platter and tent with foil to keep warm.

Add remaining 1 tbsp evoo to same skillet. Add onions and stir until beginning to soften and turn brown, about 1 minute. Add brussels sprouts, broth, cranberries, and sage. Cover and cook until brussels sprouts are crisp-tender, stirring occasionally (or just firmly shaking the pan), about 5 minutes. Stir in vinegar. Add butter; stir until melted. Season to taste with salt and pepper.

Spoon brussels sprouts mixture over turkey cutlets and serve.