In a blender or food processor, blend the milk and crushed pineapple on high until the mixture is smooth and evenly combined.
On the stovetop, heat the butter and coconut oil in a saucepan over low-medium heat just until melted. Pour the melted butter and coconut oil into the bowl of a stand mixer.
In the empty sauce pan, pour the pineapple-milk mixture and warm for 2-3 minutes over medium heat.
Pour the pineapple-milk mixture into the bowl with the butter and coconut oil. Because all 4 ingredients are warm, the coconut oil should not solidify. (If the oil begins to clump, you can warm the mixture in the microwave in 10 second increments). To the mixture, add the sugar, salt, egg, egg yolk, caramel extract, and active sourdough starter. Using the paddle attachment, mix until the ingredients are equally distributed.
Add the 3 ¾ cups of bread flour. Mix on low until the flour is combined with the other ingredients. The dough should be sticky to the touch. Cover the dough with plastic wrap and let rest for 30 minutes.
Using the dough hook attachment, knead the bread on low for 6 minutes. If the dough sticks to the bottom, stop and lightly dust with flour (additional ¼ cup). For optimal results, knead the dough by hand for 3-4 more minutes, adding flour if necessary to reduce dough stickiness.
Place dough in a lightly oiled bowl. Cover with plastic wrap and let rise until doubled in size. (I like to let mine rise in the evening for an hour or two and then I place the dough in the fridge overnight.)
Once doubled in size (or in the morning), divide the dough into 12 equal sections. If using a kitchen scale, each section will weigh approximately 84-90 grams.
Pick up one section of dough. Cup your hand lightly over it, with your fingers forming a loose cage around the dough. Gently press down and use your cupped hand to form a smooth ball. Tuck the edges underneath and place onto an oiled 12 inch X 8 inch glass baking dish or tin. Cover with plastic wrap and let rise until desired size or doubled in size. .
Preheat the oven to 375 degrees Fahrenheit (190 degrees C). Whisk an egg with a fork in a small dish. Brush the tops of the rolls with the egg with a basting brush. Bake for 24-28 minutes or until golden brown. Let cool until warm and serve with a generous helping of butter. Enjoy!