Melt the butter in the microwave for about 25 seconds, or in a small saucepan on the stove until just liquid.
Pour the melted butter into a large mixing bowl.
Add the sugar and stir to dissolve.
Sprinkle in the salt and mix again.
.Pour in the warm water.
Whisk everything together, then add the egg and whisk until smooth.
Add the dried yeast, give it a quick stir, cover the bowl and leave it for about 10 minutes so the yeast can activate.
Add the flour and knead until you get a soft, slightly tacky dough.
Shape the dough into a ball, cover it with a kitchen towel or plastic wrap and let it rise in a warm place for around 1 hour, until doubled in size.
Turn the dough out onto the counter and roll it out with a rolling pin.
Use a glass to cut out circles from the dough.
Use a plastic bottle cap to punch a smaller circle in the middle of each disc to form a donut shape.
Repeat with all the dough scraps, then leave the shaped donuts on the counter for about 10 minutes to puff slightly before frying.
Pour plenty of oil into a heavy pot or deep pan and heat it up.
Gently place the donuts into the hot oil and fry over medium-high heat.
When the bottoms turn golden, flip the donuts to cook the other side.
Line a plate with paper towels and transfer the fried donuts there to drain excess oil.
While still slightly warm, dust the donuts generously with powdered sugar.