In a large mixing bowl, add the sourdough starter, flour (start with 4 1/2 cups), sugar, active yeast, and salt. Mix well to combine, and make a well in the center of the flour mixture.
Add melted butter, milk, pineapple juice, and egg to a bowl, scramble well with a fork until combined. Add the egg mixture to the center of the flour well. Pour the warm water over the egg mixture. With a large spoon, mix well to combine all ingredients into a dough. Dough should be sticky and thick. If your dough is sticking to the sides of the bowl, add the remaining 1/2 cup flour.
Cover with plastic wrap and place bowl in the refrigerator overnight (8 to 12 hours).
The next morning, grease 2 8x8 loaf pans. Turn dough out onto a well-floured work surface.
Divide dough into 2 equal sections. And then divide each of those sections roughly into 9 equal parts. Each of those 9 parts will become one roll. I used my hands to roll the dough into balls, then placed them in the 8x8 in baking dish. Each baking dish should have 9 rolls. Cover, and allow dough to rise in the baking dishes in a warm place for 2 hours or until doubled in size (mine has taken up to 4 hours on colder days).
Preheat oven to 375 degrees Fahrenheit. Brush the tops of the rolls with egg wash (1 egg mixed with 2 tablespoons water) and place in oven to bake for 18 to 24 minutes. Top should be brown, but if it starts to look burnt, then cover with foil and continue to bake.
Allow rolls to cool on a rack for at least 45 minutes before slicing.