Place your russet potato in a small pot of boiling water, making sure there's enough water to fully submerge the potato. Boil until completely soft, about 20-40 minutes depending on its size. Remove and press through a potato ricer on the finest setting.
Combine the milk and water in a small container, heat in the microwave just until 90-95°F (32-35°C), no warmer or cooler. Whisk in your yeast and sugar and let sit until dissolved and foamy, about 2 minutes.
In the bowl of a stand mixer, whisk together bread flour, salt, amylase, and turmeric. Pop onto your stand mixer with the dough hook. While mixing on low speed, add your yeast mixture, oil, whole egg, egg yolk, and finally the cooked and cooled mashed potatoes. Mix for 5 minutes, stopping and scraping down the sides of the bowl as needed until you get a smooth and elastic dough.
Press in your softened butter and allow to incorporate. Mix until extremely smooth, another 2-3 minutes.
Grease your hands then transfer to a greased bowl, cover with plastic wrap (or a damp towel), and let rise at room temperature for 1 ½-2 hours, or until doubled.
Punch down then use a flexible bench scraper to remove your dough to a work surface. Divide into 10-12 pieces that weigh about 105g each.
Preheat your oven to 375°F (191°C). Shape each dough into a nice taught ball. Place the ball on lightly greased parchment lined baking sheets evenly spaced apart.
Cover with greased plastic wrap and rise for 30-60 minutes or until the dough is nearly 1.5 times in size.
Brush each bun with a light layer of whole milk to fully coat each bun, then bake for 15-17 minutes, or until lightly browned.
Remove and immediately brush with melted butter. Allow to cool completely on wire racks.
