Arancini di Riso con Funghi (Mushroom Arancini)

Ingredients

• 500 gm arborio rice
• 3 large eggs, beaten
• 40 gm butter, coarsely chopped
• 50 gm finely grated parmesan
• 2 tbsp olive oil
• ½ onion, finely chopped
• 1 garlic clove, finely chopped
• 200 gm chestnut mushrooms, trimmed
• 1 tbsp coarsely chopped flat-leaf parsley
• 60 gm Ragusano, coarsely grated (see note)
• For deep-frying: vegetable oil
• 200 gm fine fresh white breadcrumbs
• To serve: saffron aioli (see note)