In a microwave-safe small bowl or measuring cup, add the milk and pineapple juice together. Heat in the microwave or on the stove until the liquid measures around 105 to 115º Fahrenheit. Don't worry if the liquid is a little lumpy. Mix in the yeast and honey. Set the mixture aside for 5 to 10 minutes or until the yeast is nice and foamy.
In a stand mixer or large bowl, whisk together sugar, salt, and 3 cups of flour. Add in the yeast mixture, eggs, and melted butter. Mix on low speed until everything is well combined.
If the dough is still extremely wet, add the additional cup of flour, mixing in half a cup at a time. If the dough is still sticky to the touch after the fourth cup of flour, add a few tablespoons more, mixing well after each addition. The key is to get a dough that is slightly sticky but that bounces back after it is lightly pressed. Continue to mix for 3 to 4 minutes on low speed.
Remove the dough from the mixer and place it in a large, lightly oiled bowl. Cover with plastic wrap or a kitchen towel and allow to sit in a warm location until it has doubled in size. This usually takes about an hour.
Meanwhile, butter a 9 x 13 glass baking dish or pan and set aside.
Once the dough has doubled, divide it into 12 equally-sized pieces. Form the dough into smooth balls and place in the prepared baking dish in three rows of four. Cover the dish and allow the rolls to rise for about 30 to 40 minutes or until they have puffed out slightly.
While the rolls are rising, preheat the oven to 375º Fahrenheit. Right before baking, mix together the egg white and melted butter in a small bowl. Brush the tops of each bun with the egg wash.
Bake the rolls in the preheated oven for 20 to 25 minutes or until the rolls are slightly browned on top. Remove from oven.
In a small bowl, mix together the melted butter and honey to make the honey glaze. Brush this on the rolls immediately after removing them from the oven.
Serve warm or at room temperature. Store any cooled leftover rolls in a plastic bag or sealed container. Enjoy!