In the bowl of a stand mixer, whisk together the yeast, milk, water, and sugar. Set aside until foamy, about 10 minutes.

Once foamy, stir in the mashed potatoes, melted butter, and egg.

In a medium bowl, whisk together the all-purpose flour, bread flour, and garlic powder.

Stir ½ cup of the flour mixture into the yeast mixture until a thick paste forms.

With the mixer on low speed, beat in the salt and the remaining flour mixture, ¼ cup at a time. Mix until the dough is soft and pulls away from the sides of the bowl, 3 to 5 minutes.

On a lightly floured surface, knead the dough for an additional minute. Then form into a large ball. If the dough is too sticky, add more flour as needed.

Grease a large bowl with the olive oil and place the dough inside. Roll the dough in the oil to completely coat. Cover the bowl with a clean cloth and let rest at room temperature until doubled in size, 1 to 2 hours.

Preheat the oven to 350F. Line 2 baking sheets with parchment paper and lightly grease the paper.

On a lightly floured surface, divide the dough into 18 portions and shape each portion into a ball. Keep the dough covered with a clean cloth to prevent a skin from forming.

Roll the balls into 4-inch ropes with a bulge at each end. Place on the baking sheets.

Cut the ends of the breadsticks to create bone details.

Cover the breadsticks with a clean cloth and let rest for 15 minutes.

Bake the bones until golden brown, 12 to 14 minutes.

In a small bowl, stir together the melted butter and garlic powder.

Brush the garlic butter onto the warm breadsticks and sprinkle with the Asiago.