In a medium-sized mixing bowl, combine the dry ingredients: flour, yeast, and caster sugar. Mix thoroughly with a spatula.
Add the egg yolks to the dry mixture and begin to incorporate them. Gradually pour in the milk and softened butter. Continue mixing until a smooth dough forms.
Once the dough comes together, shape it into a ball. Cover the bowl with a clean kitchen towel and place it in a warm, draft-free spot to rise for 2–3 hours or until the dough has doubled in size.
Once the dough has risen, turn it out onto a floured surface.
Roll the dough to about ½-inch thickness. Use a round cookie cutter to cut out circles of dough.
For the donut holes, use a smaller cutter (approximately ¾ inch) to cut out the center of each circle. Save the donut holes for frying, too!
Place the shaped donuts onto a parchment-lined baking sheet and let them rest for another 30 minutes to rise slightly.
Heat vegetable oil in a deep pan or deep fryer to 350°F (175°C). The oil should be deep enough to fully submerge the donuts.
Carefully lower 1–2 donuts into the hot oil using a slotted spoon or tongs. Fry for about 1–2 minutes on each side until they are golden brown.
Remove the donuts from the oil and place them on a paper towel-lined plate to drain excess oil. Repeat with the remaining donuts and donut holes.
In a small bowl, mix the icing sugar with 2 tablespoons of water until smooth. The glaze should have a thick yet pourable consistency. If it’s too thick, add a few more drops of water.
Once the donuts have cooled slightly, dip the top of each donut into the icing or drizzle the glaze over them.
While the glaze is still wet, generously sprinkle the donuts with orange, pink, and white sprinkles. Let the glaze set for 10–15 minutes before serving.