In a large bowl, combine the thyme, paprika, Cajun seasoning, oregano, olive oil, salt, pepper and sugar. Fold in the potato wedges, cover, and refrigerate for 30 minutes.
Preheat the oven to 450°F.
Transfer the seasoned potatoes to a baking sheet and roast for 15 minutes, or until crisp.
In a large bowl, gently combine burger ingredients until well mixed. Form into 4 patties.
Heat the oil in a skillet over medium heat. When hot, add the patties and cook for 4 minutes. Flip and repeat on the other side, until cooked to your desired doneness.
Serve the burgers on brioche buns with pickles and aioli.