Prepare the Crab Mixture: Drain crab meat and check for shells. In a separate bowl, mix mayonnaise, egg, Dijon, parsley, bell pepper, celery, green onions, Old Bay, salt, and pepper. Gently fold into crab meat, then gradually add gluten-free breadcrumbs until mixture holds together.
Form & Chill the Crab Cakes: Divide mixture into 8 equal portions. Form into patties about 3 inches wide and 1 inch thick. Place on parchment-lined baking sheet and refrigerate for at least 30 minutes.
Cook the Crab Cakes: Heat oil in a large skillet over medium heat. Cook crab cakes in batches for 3-4 minutes per side until golden brown. Transfer to paper towel-lined plate.
Prepare the Aioli: Whisk together mayonnaise, lemon juice, garlic, and dill. Season with salt and pepper to taste.
Serve: Plate crab cakes with a dollop of aioli and lemon wedges.