In a shallow baking dish, combine the flour, Parmesan, paprika, mustard, oregano, salt and pepper and stir until well blended. Pour the milk in a shallow bowl.
Working with 1 wing at a time, dip the chicken in the milk, then dredge it in the flour mixture, and then tap off any excess flour. Place the wings on a plate.
In a deep-fryer, deep-sided skillet, or Dutch oven, heat about 2 inches peanut oil until it registers 350°F (177°C) to 365°F (185°C) on a deep-fry thermometer. Fry the chicken wings in small batches, being careful not to crowd the pan, nudging the wings so they don’t stick to the pan and turning them if necessary, until golden brown and cooked through, 8 to 10 minutes. (If the chicken wings are especially meaty, they may require a minute or so longer, just be careful not to fry them so long that they dry out.) Using tongs, transfer the wings to paper towels to drain. Rest assured, these chicken wings are just as good at room temperature as they are hot.