Add mashed butternut squash and milk in a stand mixer, mix them with a spatula to roughly combine.
Add yeast, bread flour, cake flour, sugar and honey (or sweetened condensed milk) into the stand mixer, mix with medium low speed until it forms a rough dough (see the picture in the post). Cover and let it rest for 20-30 minutes.
Meanwhile, take the butter out from the fridge and cut it into 6 pieces and set it aside.
When it's done resting, add salt and continue to knead the dough for 1 minute.
Add butter cubes one at a time and knead until the dough is silky smooth and passes the windowpane test. (This step takes me about 8 minutes on medium speed. The actual time it takes you depends on your mixer.) Since the dough is very sticky, you probably need to scrape down the dough on the sides of the mixing bowl one or two times in the mixing process.
Form the dough into a ball (it will be very sticky, but if it's too sticky to handle, then add a little bread flour and knead for another 1~2 minutes) and put it in a lightly greased bowl. Cover, and let it rise for about 1 hour in a warm place (between 80°F to 90°F) until it doubles in size.
Transfer the dough onto a working surface and cut it into 20 (or less if you prefer the roll to be a bit bigger) even pieces. Cover and let them rest for 5 minutes.
Form each piece into a ball and place them in a lined baking pan with ¼-½" apart.
Cover with greased plastic wrap and let it rise in a warm place (between 80°F to 90°F) until it doubles in size (about an hour).