Heat buttermilk for 40 seconds in the microwave until the liquid reaches 100-110 degrees F (38-43 degrees C). I like to do this in a liquid measuring cup. Add the yeast and sugar and mix.
Next, add butter to a large bowl. Pour the sugar/buttermilk mixture into the bowl. Whisk with a hand mixer or stand mixer until the butter has broken down.
Add the egg, salt, and ube extract. Mix until incorporated.
Lastly, add the flour and combine until a dough forms.
Empty the dough onto a floured surface. Knead for 10 minutes. You can also knead the dough in a stand mixer for the same amount of time. If the dough still seems wet, add a tablespoon of flour at a time until it doesn’t stick to your hands. It can be normal to add 1/4 cup to 1/2 cup more flour.
Cover with a wet towel or plastic wrap and let the dough rise in a warm place for 1-2 hours until it doubles in size.
Once the dough is done proofing, punch out the air. Then roll it out into a 12×12 inch square. Smear the top of the dough with ube halaya. Top with brown sugar and cinnamon.
Roll into a log and cut into 9 equal pieces. Cut the log into 3 equal pieces and then divide each piece into 3 equal pieces.
Place the cinnamon rolls into a greased 9×9 pan. Let the dough rise for 1-2 more hours.
Preheat the oven to 350 degrees F (177 degrees C).
After the last proof (rise), bake for 20-25 minutes uncovered until the edges are light brown.
While the cinnamon rolls are baking, combine all the ingredients for the glaze and mix. Set aside.
Cool for 5-10 minutes before adding the glaze.