Preheat grill to 400°F / 200°C.
Cut potatoes into wedges – slice the potato in half lengthwise, then cut each piece in half again to create quarters. Cut each quarter in half or into thirds if the potato is very large.
In a medium mixing bowl, toss potato wedges with oil and set aside.
In a small mixing bowl, combine all ingredients for Cajun spice blend and whisk to combine thoroughly.
Sprinkle 1 1/2 - 2 tablespoons of the spice blend over the potato wedges and toss to combine. (Use less if you don't like strong seasoning, more if you do)
Place potato wedges on grill and cook for 10 minutes. Flip potatoes over and cook for an additional 10 minutes (lowering temperature of the grill if they are starting to get too dark), or until potatoes are cooked through.
Make dipping sauce by combining 1/2 cup mayonnaise with 1 1/2 teaspoons of spice blend and stir to combine.
Serve warm with dipping sauce, if desired.