In a medium bowl, combine the self-rising flour, active dry yeast, and caster sugar.
Add the egg yolks, milk, olive oil, and melted butter. Mix until a soft dough forms.
Knead the dough lightly until smooth, then cover the bowl with a kitchen towel and place it in a warm spot to rise for about 2 hours, or until doubled in size.
Lightly flour a work surface. Roll the dough out and cut rounds using a large round cutter. Use a ¾-inch cutter to cut holes in the center of each donut.
Heat the neutral oil in a deep pot or deep fryer to 350°F. Carefully fry 1–2 donuts at a time for about 2 minutes per side, or until golden brown. Transfer to a plate or wire rack to cool slightly.
To make the icing, whisk together the powdered sugar and water in a small bowl until smooth.
Spoon or drizzle the icing over each donut, then immediately decorate with the orange, pink, and white sprinkles. Serve fresh and enjoy!