Preheat oven to 450 degrees F. Line a large baking sheet (or two smaller sheets) with parchment paper; set aside.
In a mixing bowl, whisk together all remoulade ingredients until well combined; set aside.
Cut washed potatoes into 1⁄4-inch strips and place in a large bowl or gallon-sized resealable bag, pour olive oil on top and toss to coat. Spread cut potatoes in an even layer on baking sheet(s) and bake for 25-30 minutes or until golden brown and crisp.
In a small bowl, whisk together salt, Parmesan cheese, minced garlic, cajun seasoning and fresh parsley then sprinkle on top of fries and toss before serving with remoulade.