Wash the oranges with hot water, rub off some of the peel. Fillet the fruit carefully. Squeeze the lemon juice. Halve the avocado, remove the stone and remove the pulp from the skin.
Immediately put the orange fillets, lemon juice, the avocado meat and the honey in the blender and puree until smooth on the highest setting. Pour in the buttermilk and mix briefly on the lowest setting. Transfer to glasses.