How to Make It
In a food processor, pulse 3/4 cup of the walnuts with the bread crumbs and cheese until the walnuts are finely ground. Transfer to a shallow bowl and season with salt and pepper.
Wipe out the bowl of the food processor. Add the remaining 1/2 cup of walnuts along with the sage and garlic and pulse until the nuts are coarsely chopped. Add the butter and 1/3 cup of the olive oil and process until the nuts are finely chopped and the butter is incorporated. Season the sauce generously with salt and pepper and transfer to a small bowl.
Put the flour and eggs in 2 shallow bowls. Season the turkey cutlets with salt and pepper, then dust them with flour, tapping off the excess. Dip the cutlets in the beaten eggs, letting the excess drip back into the bowl. Dip the cutlets in the walnut-crumb mixture, pressing to help the crumbs adhere.
In a very large skillet, heat 3 tablespoons of the olive oil until shimmering. Add half of the cutlets and fry over moderately high heat, turning once, until golden outside and cooked through, about 3 minutes. Transfer the cutlets to a paper towellined plate to drain. Repeat with the remaining olive oil and turkey cutlets. Transfer the cutlets to plates, spoon some of the walnut-sage sauce on top and serve at once.