The day before serving, heat milk to 110° and sprinkle yeast on top. Allow to proof or get foamy. (If using instant yeast, there’s no need to activate the yeast. Instead, make sure all ingredients are room temperature, not chilled.)
In a medium glass bowl, melt butter. Into a stand mixer fitted with the dough hook, add in butter, sugar, salt, and egg. Mix until combined. Add in yeast mixture and mix once more to combine. Reserve buttered bowl.
In a small bowl, whisk together flours and potato starch. Slowly add in flour and begin mixing the dough on low to medium speed. Once incorporated, continue mixing for 8 minutes to develop gluten in the dough. If dough is too dry, add one tablespoon of milk at a time. Dough should feel soft but not sticky.
Return dough to buttered glass dish. Cover and a let rise for 2-3 hours or until doubled in bulk.
Punch down dough. Remove from bowl and cut into 12 equally sized pieces. Begin forming into balls by pulling and gathering the dough at the bottom to hide the seam. Place in a 9-inch circle pan. Cover with plastic wrap and place in fridge overnight. (If baking the same day, skip the fridge, and allow to double in size, covered, at room temperature. About one hour).
About 2 hours before serving, remove rolls from fridge and allow to come to room temperature and rise.
Preheat oven to 375°. Stir together butter mixture in a small bowl. Just before baking, brush butter over the tops of the rolls reserving a small amount for afterwards.
Bake for about 17 minutes. Remove from oven and brush any remaining butter on the top. Carefully pull apart rolls and serve.
PS—I recommend investing in SAF Active Yeast. It’s been nearly fool proof for me and doesn’t take activation to work, although I still allow it to proof sometimes to calm my nerves. Also, for more information on the different types of yeast and how they work, check out The Kitchn.