Preparation:
To prepare Avocado Serrano Aioli: In jar of blender, place 1/2 cup of the mayonnaise, 1 chile, garlic, 2 tablespoons of the lime juice, 1 avocado; puree until smooth. Season to taste; cover and refrigerate up to 12 hours in advance.
To prepare Crab Cakes: In bowl, mix together mustard, egg, onion, remaining mayonnaise, lime juice and chile. Add crabmeat, breadcrumbs, salt and pepper; combine well.
Shape about 3 tablespoons of crab mixture into a 3/4-inch thick cake. Repeat with remaining crab mixture. Refrigerate for up to 2 days.
In large skillet, heat butter and oil over medium- high heat. Once butter begins to sizzle, add crab cakes in batches; cook until crisp and golden brown, about 5 minutes per side.
To serve, spoon Avocado Aioli on top or on the side; garnish with avocado slices.