If baking, position a rack in the center of your oven and preheat to 425°F. If air frying, preheat the air fryer to 400°F.
Peel the outer fibrous layer from the broccoli stems using a vegetable peeler. Slice the stems lengthwise into strips about 1/8 to 1/4 inch thick. If the stems are longer than 6 inches, cut them in half crosswise to make handling easier.
In a medium bowl, combine Parmesan, panko breadcrumbs, garlic powder, salt, and paprika. Set up a breading station by pouring some olive oil into a shallow bowl and transferring 1/3 of the panko mixture into another shallow bowl.
One by one, dip the broccoli strips into the olive oil, then dredge them in the panko mixture, pressing gently to coat. Arrange the coated strips on a baking sheet in a single layer. Refill the panko bowl as needed.
If oven-baking, bake for 10–12 minutes, flipping the fries halfway through until golden and crispy. If using an air fryer, cook the fries for about 5 minutes per batch, ensuring the strips don’t overlap.
Transfer the cooked fries to a serving platter and sprinkle with a pinch of salt. Serve immediately with ranch or Caesar dressing for dipping.