Generously grease a 13×9-inch baking dish with oil. Set aside.

In a small bowl, mix brown sugar and cinnamon for the filling. Set aside.

In a large bowl, combine 1½ cups gluten-free flour and yeast.

In a saucepan, heat milk, mashed potato, butter, sugar, and salt until warm (120–130°F), just until butter melts.

Add warm mixture and eggs to flour mixture. Mix with an electric mixer for 30 seconds on low, then 1 minute on medium-high until smooth.

Gradually add remaining flour until dough is soft, pliable, and not sticky. Do not overmix.

Roll dough into an 18×12-inch rectangle.

Spread softened butter over dough, sprinkle cinnamon-sugar filling evenly, leaving 1 inch bare on one long side.

Roll tightly into a log, pinch seam closed, and slice into 12 rolls.

Place rolls in prepared pan. Cover and let rise in a warm place for 1 hour, until nearly doubled.

Preheat oven to 350°F.

Bake for 30–35 minutes, until golden and center reaches 200°F.

Cool 10 minutes. Mix frosting ingredients until smooth and spread over warm rolls. Serve and enjoy.