For the sweet potato fries: Preheat the oven to 425 degrees F; place a baking sheet in the oven to preheat. Place the sweet potato wedges in a bowl and toss to coat with the oil, brown sugar, salt and pepper. Place on the preheated sheet tray and bake until slightly crisp and beginning to brown, 25 to 30 minutes.
For the garlic aioli: Meanwhile, mix together the garlic, lemon juice, mayonnaise, paprika and salt and pepper to taste. Serve the fries with the aioli on the side to dip.