Combine water, poi, butter, egg, yeast, and purple food coloring in the bowl of a stand mixer fitted with the dough hook. Let stand until yeast softens and forms a creamy foam, about 5 minutes. Add sugar and salt.
Mix on low speed, adding flour gradually, until dough comes together and texture is smooth.
Turn dough out onto a floured work surface. Divide into 18 pieces; shape into rolls.
Preheat oven to 325 degrees F (165 degrees C). Line a baking sheet with aluminum foil.
Place rolls on the prepared baking sheet. Cover and let rise until doubled, about 20 minutes.
Bake in the preheated oven until bottoms start to brown, about 20 minutes.