Start by making your garlic aioli sauce. In a small bowl mix mayonnaise, minced garlic, lemon juice, salt and pepper. Refrigerate for 15 minutes or overnight.
Preheat Grill or Panini Press.
In a large bowl add the ground turkey, egg, milk, panko crumbs, oregano, garlic powder, salt, pepper and Chèvre cheese. Mix well. Divide the mixture and form into 4 equal sized patties.
Spray grill with oil and cook for 8-10 minutes, turning halfway, or until the turkey patties are golden brown and fully cooked.
Butter the inside of each Brioche bun and toast on a heated non-stick pan or grill for 1-2 minutes, until golden brown. (Trust me, this step is WORTH IT!)
Spread garlic aioli onto each of the toasted Brioche buns. Add your turkey patty and any other toppings you wish (lettuce, red onion, tomato). Serve immediately with a salad or fries.