In the bowl of a stand mixer, add the softened butter, pineapple juice, brown sugar, vanilla extract, potato flake sourdough starter, salt, flour, and the whole egg, plus one yolk. Save the egg white in a small bowl for the egg wash.
Mix on low for about 4 minutes until the dough starts pulling away from the bowl. Then switch to medium-high speed and knead for 5 more minutes until the dough forms a smooth ball. It should feel soft, slightly tacky but not sticky.
Remove dough from the bowl and shape into a tight ball. Use the counter to help create tension on the surface of the dough ball by pulling the ball towards you and moving in a circular motion.
Grease a large bowl or the mixing bowl used, and place dough into the bowl, turning to coat. Cover with a bowl cover or plastic wrap and place in a warm place to rise for 8 hours, or until doubled.
Gently deflate the dough to remove air bubbles. Shape into a round loaf and place in a floured lined banneton basket or a bowl with a floured tea towel.
Cover the bread dough with plastic wrap or a clean plastic bag to prevent the dough from drying out. Set in a warm place to rise, about 4-6 hours or until doubled in size.
Carefully transfer the risen dough onto a parchment lined rimmed baking sheet, round cake pan, pizza stone or loaf pans (if making into loaves). The best way is to place the parchment paper and pan over the basket and carefully but quickly flip the bowl and pan over together at the same time to prevent the dough from deflating.
Beat the egg white with 1 T of water and use a pastry brush to gently brush the egg wash over the loaf.
Bake in a preheated 350°F oven for 20 minutes uncovered, then loosely cover with foil and bake another 20 minutes. Check for doneness with an instant-read thermometer—look for 190°F internally.
Let cool on a wire rack slightly before slicing. Serve warm or at room temperature.