Heat oven to 200 degrees.
In a medium size microwave safe bowl (or a 2 c. glass measuring cup), combine the butter, buttermilk, pineapple juice and brown sugar. Heat in the microwave until the mixture is hot and the butter is almost melted (it took about 1 minute 40 seconds on HIGH in my microwave). Allow to sit for 3-4 minutes on the counter until it cools and reaches approximately 110 degrees, then add the extracts.
Meanwhile, in the bowl of a stand mixer, combine the 3¾ c. flour, yeast, salt and ground ginger. Using the paddle attachment, turn the mixing speed on low and slowly pour in the wet ingredients. Continue mixing while adding the eggs and egg yolk. A sticky dough will begin to form. Switch to the hook attachment and knead the dough for 7-8 minutes, adding 1/4 c. more of flour if necessary. Do note that this is a very sticky dough, so don't add any more than 4 c. of flour total! Once the dough has been kneaded, form into a ball and place in a large metal or glass bowl that has been lightly greased. Cover with a clean towel, turn OFF your oven, place inside and allow to rise for 1-1½ hours or until doubled.
Once the dough has doubled, remove and gently deflate. Divide into 12 equal pieces. Roll into circles and place in a parchment lined 9x13 pan or ¼ baking sheet. Heat oven to 200 degrees. Generously butter the tops and sides of each roll. Place a clean kitchen towel over top. Turn OFF your oven and place the covered rolls inside to rise for 1-1½ hours or until doubled.
Remove the rolls from the oven and turn ON your oven to 350 degrees. Once heated, bake the rolls for 22-25 minutes or until the tops are golden brown in color.
Remove from the oven and brush with the remaining butter. (SEE NOTES)