Preheat the oven to 375 degrees F. Line 2 baking sheets with parchment paper.
Place the turkey wings in a large mixing bowl. Pour in the oil and barbecue spice blend. Massage the wings until evenly coated on all sides. Place the seasoned wings on the prepared baking sheet. Set the oil remaining in the bowl aside. Roast until the wings reach an internal temperature of 165 degrees F and are golden brown and crispy, about 1 hour 20 minutes.
Meanwhile, prepare the barbecue sauce: In a small saucepan over medium heat, pour in the oil remaining from the bowl the wings were tossed in. Add the shallot and garlic. Cook until softened, 3 to 5 minutes. Add the peaches, tomato paste and maple syrup. Cook, stirring frequently, until the mixture begins to caramelize. Pour in the stock and stir to combine. Reduce the heat to medium low. Simmer, stirring occasionally, until slightly thickened, about 20 minutes. Stir in the Worcestershire sauce and paprika. Use an immersion blender to puree the mixture until smooth. Add kosher salt to taste.
Remove the wings from the oven and brush generously with the sauce. Return to the oven and broil for 3 minutes, until the sauce bubbles and begins to brown. Serve immediately garnished with parsley and with extra sauce as desired.