Preheat your oven to 425°F and line a baking sheet with parchment paper, placing a wire cooling rack on top.
Pat the chicken wings thoroughly dry with paper towels to ensure the skin becomes extra crispy during baking.
In a large mixing bowl, toss the wings with the baking powder, sea salt, black pepper, garlic powder, and smoked paprika until every wing is evenly coated.
Place the wings in a single layer on the wire rack and bake for 35 to 40 minutes, flipping them halfway through the cooking time.
While the wings are in the oven, whisk together the tomato paste, apple cider vinegar, honey, and cayenne pepper in a small saucepan over low heat until the sauce is smooth and warm.
Remove the crispy wings from the oven and transfer them to a clean bowl, then pour the spicy BBQ sauce over them and toss until they are well glazed.
Cut the celery and carrot into thin sticks and serve them immediately alongside the hot, spicy wings.