Heat oil and butter in a medium saucepan over medium heat. Add onion and cook for 5 minutes, stirring often, or until softened. Add rice, stir well and cook for 2 minutes. Gradually stir in 1/2 cup stock, stirring until absorbed. Continue adding stock until creamy and rice is just tender.
Transfer to a bowl and stir in basil and parmesan. Cool for 5 minutes then stir through egg. Chill for 30 minutes. With damp hands, roll tablespoonfuls of rice into balls and place on a baking paper-lined tray.
Place breadcrumbs in a deep bowl. Add arancini, tossing well to coat in crumbs. Return to tray. Heat oil in a medium pan over medium heat. Slice salami into 3 long strips.
Deep fry arancini balls, in batches, for 3-4 minutes or until golden brown. Drain on paper towel. Wrap each ball with a strip of salami, securing with a toothpick and garnish with basil leaves and serve with aioli.