Melt the butter in a microwave safe bowl. Add the milk and beer. Heat until 120°-130°F (if your yeast packet mentions a different temperature, use that temperature instead).
In the bowl of a stand mixer, stir together the flour, yeast, sugar and potato flakes.
Add the beer mixture, stirring on medium speed until most of the flour has been moistened. Add the salt and egg, stir until well combined and the dough gathers around the blade.
Oil a large bowl. Using wet hands, move the dough to the bowl. The dough will be very soft and sticky.
Cover and allow to rise until doubled in size, about 45-60 minutes.
Preheat oven to 350°F.
On a well-floured surface add the dough. Cut into 12 equal sized pieces.
Roll into tight balls, add to a baking pan sprayed with cooking spray.
Cover and allow to rest until doubled in size.
Brush with egg wash, sprinkle with salt.
Bake uncovered until golden brown, about 25 minutes.