Cut potatoes in half lengthwise and then quarter each half to create 16 wedge fries per potato. Rinse cut potatoes under cold running water and pat dry.
Arrange potatoes onto a baking sheet and drizzle with oil and Cajun seasoning. Toss until well combined and arrange into a single layer, careful not to overcrowd. Roast potatoes in the oven for 45−50 minutes uncovered, shaking the pan and flipping the fries on occasion to brown on all sides. Serve warm with ketchup or basil-balsamic mayo.