Peel and cut the russet potato into 1/2-inch pieces.

Place the potato pieces in a medium saucepan and cover with 2 1/2 cups of water.

Bring to a boil and cook until the potato pieces are very tender, about 15 minutes.

Drain the potatoes, reserving 1 1/4 cups of the potato liquid in a separate bowl.

Cool the potato liquid until it is lukewarm (110 to 115 F).

Add the active dry yeast to the lukewarm potato liquid and let it sit for 10 minutes to activate.

Mash the cooked potato pieces until smooth.

Measure out 1/2 cup of the mashed potato.

In an electric mixer fitted with the paddle attachment, combine the yeast mixture, mashed potato, granulated sugar, 1 1/2 teaspoons of salt, 6 tablespoons of melted butter, and the egg.

Mix on low speed for 15 seconds to combine.

Add 2 cups of all-purpose flour and mix on low speed until thoroughly blended, about 1 minute.

Switch to the dough hook attachment.

Add 2 1/2 cups of flour and knead at medium speed, adding more flour as needed to make a soft, elastic dough, about 10 minutes.

Scrape the dough into a large plastic bag, ensuring there's enough room for expansion.

Seal the bag and place it in the refrigerator to rise overnight.

Turn out the dough onto a lightly floured surface and knead it a few times to soften.

Divide the dough into 16 equal pieces and roll each portion into a smooth ball.

In a large, shallow bowl, mix together 8 tablespoons of melted butter and the remaining 1/4 teaspoon of salt.

In a separate large, shallow bowl, mix the brown sugar and ground cinnamon.

Dip each dough ball (bun) in the butter, coating the entire surface, and then roll it in the brown sugar and cinnamon mixture, ensuring it's well coated.

Grease a 9 x 13-inch baking dish with the remaining 1 tablespoon of butter using a pastry brush.

Place the coated buns in the prepared dish, cover them with oiled plastic wrap, and let them rise in a warm, draft-free place until they are 1 1/2 times their original size, about 45 minutes to 1 hour.

Preheat the oven to 350 F.

Bake the buns for about 25 minutes, or until they are light golden on top and a toothpick inserted into the center bun comes out clean.

Remove the buns from the oven and immediately turn them out onto a serving platter.

Let the buns cool for at least 5 minutes before serving.

To serve, cut apart the buns.

Place each bun on a small plate and drizzle with the syrup from the bottom of the baking dish.

To freeze the buns, let them cool completely, wrap them tightly in plastic wrap, and freeze for up to 1 month.

To reheat frozen buns, unwrap them and bake them in a 350F oven for about 30 minutes.