Place cut potatoes in a large bowl and submerge in cold water for 30 minutes.
While the potatoes soak, mix together the salt, paprika, onion powder, ground mustard, and garlic pepper in a small bowl until thoroughly combined. Set aside.
Place the oil in a deep fryer or a 5-quart pot and preheat to 350°F.
Drain the potatoes and spread them in a single layer on two baking sheets, lined with paper towels.
Place paper towels over the potatoes and gently press to remove any excess water.
In batches, blanch the potatoes for 2-3 minutes and drain onto paper towels.
Once all the potatoes have been blanched, set aside and bring the temperature of the oil up to 365°F.
Place all the aioli ingredients in a food processor and process until smooth.
Transfer to a small bowl, adjust seasonings and cover until ready to use.
In batches, fry the blanched potatoes for 5-7 minutes or until golden brown, carefully stirring to prevent sticking.
Drain onto paper towels and sprinkle liberally with the paprika seasoning blend. Gently toss until well combined.
Serve hot with a side of the aioli for dipping.