In a large bowl, whisk together the flour, sugar, salt, and yeast. Ensure the yeast doesn't come into direct contact with the salt, as it can slow down its activation.
Add the warm milk, melted butter, eggs, and poi puree. Mix with a wooden spoon or by hand until the dough comes together.
Knead the dough for about 10 minutes until it becomes elastic and smooth. If it's too sticky, add a little flour, but be careful not to make it too stiff.
Cover the dough with a kitchen towel and let it rise in a warm place for about 1 hour, or until doubled in size.
Once risen, turn the dough out onto a floured surface and roll it out to about 1 cm thickness. Use a doughnut cutter or a glass to cut out circles, then use a smaller cutter to make a hole in the center.
In a large saucepan or deep fryer, heat the oil to about 350°F (180°C). It's important that the oil isn't too hot, as the dough can brown quickly on the outside but remain raw inside.
Fry the doughnuts for about 1-2 minutes per side, until golden brown. If they are browning too quickly, reduce the oil temperature.
Remove the fried doughnuts and place them on a paper towel-lined plate to drain excess oil.
While still warm, dust generously with powdered sugar and serve immediately!
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