Prepare the wings by cutting through the joints and splitting the drumette from the wingette. If your chicken wings come with wing tips, cut through this joint as well and discard the tips (or save them for stock).
Preheat a deep fryer or a large Dutch oven half full of vegetable oil over medium-high heat.
Once the oil has reached 350°F (180°C), carefully fry half the batch of wings, loosening up the pieces in the hot oil to make sure no wings are stuck together, as this may cause uneven cooking. Fry each batch of wings for a total of 7 minutes or until golden brown and crispy. Drain from the oil and transfer to a metal bowl. Immediately toss the first half of wings with 2 tablespoons (30 mL) hot sauce. The objective is to coat the wings evenly with hot sauce. Keep warm. Repeat with the remaining half of the wings.
Serve immediately with Parmesan dip and celery sticks.
Place all the ingredients for the Parmesan dip in a mixing bowl and whisk until they are combined. Transfer to an airtight container and refrigerate. You can store this Parmesan dip for up to a week in the fridge.
