Bring the vegetable stock to a simmer in a medium saucepan over medium heat. Slowly whisk in the instant polenta, reduce the heat, and cook about 10 minutes, stirring frequently, until thick and smooth.
Stir in the butter, half the parmesan, salt, and pepper until smooth with no lumps.
Spread the polenta evenly into a parchment-lined rectangular pan. Refrigerate at least 1 hour (overnight is best) until completely firm.
Turn the block out onto a cutting board and cut into thick, uniform sticks, about 1″ x 3″. Lightly spray or brush all sides with oil. For extra crunch, toss the sticks in a light dusting of cornstarch first.
Preheat the air fryer to 400°F. Arrange the fries in a single layer with space between each. Air fry 12–15 minutes, flipping at the 7–8 minute mark, until golden and crisp. Work in batches if needed.
Sprinkle with the remaining parmesan and serve hot with your favorite dip.