Add the peeled and chopped Yukon potatoes to a saucepan. Fill the pot with cold water. Bring the pot to a boil, and cook the potatoes for 20-40 minutes or until fork tender. Drain the water.
Add the cooked potatoes, whole milk, and unsalted butter to the bowl of a stand-mixer. Using the whisk attachment, whip the potatoes until no-lumps appear.
Switch to the hook attachment. Add bread flour, all-purpose flour, yeast, and sugar and mix on medium speed, scraping along the sides and bottom of the bowl if needed. Continuing mixing until a sick dough forms, 2 to 4 minutes.
Lower the speed, add in the eggs and egg yolks one at a time and lastly add in the kosher salt. If needed, add more flour until the dough is smooth. Mix on medium-high for approximately 5 to 7 minutes.
Grease a large bowl with butter. Transfer dough to the greased bowl and brush the dough with butter. Cover the bowl with plastic wrap and let rise in a warm area for 1 hour or until the dough doubles in size.
Punch the dough to deflate. Turn out the dough onto a lightly floured surface. Divide the dough into 18-22 equal sized pieces. Roll each dough into a smooth ball using the palm of your hand.
Line a large baking pan with parchment paper and lightly grease. Place the balls in the pan with half an inch to an inch between them. Cover and let them rise for 45 minutes to 1 hour.
Preheat the oven to 400 degrees F. Brush the tops of the dough with melted butter. Bake the rolls for 15-25 minutes, or until deep golden brown.
Honey Sage Butter: While the rolls bake, in a small saucepan over medium-high heat. Add in the butter and sage. Allow the butter to melt with occasional stirring of the pan. Cook the sage butter for 5-8 minutes. The butter will begin to brown when foam occurs with a nutty scent. Remove the butter from the heat. Discard the sage leaves. Mix in the honey.
Brush the baked rolls with the honey sage butter. Sprinkle with flaky salt. Allow to cool on a cooling rack for 20 to 30 minutes before serving.