In a kitchen aid stand mixer bowl, add both flours, potato flour, salt, sugar, oil, yeast and water to form a soft supple dough.
Add, cheese, and peppers and mix on medium-low speed with the hook until the dough holds together, about 2 minutes. The dough should clean the sides of the bowl.
Increase speed to medium and knead the dough for 5 minutes.
Transfer the dough to a large bowl that has been lightly greased with oil.
Cover it with a damp towel and let rise in a warm place until doubled in bulk, 1-1 ½ hours.
Line a baking sheet with parchment.
Turn out the dough onto a lightly floured surface.
Divide the dough into 8 medium sized rounds as well as 1 small round. Roll into rounds and flatten with the palm of your hand onto the baking sheet; placing buns about ½-1 inch apart.
Cover with a damp towel and let them rise for 30 minutes. By the end of second rise preheat the oven to 350F
Whisk the egg with 1 tablespoon water.
Brush the buns with the egg wash and bake for 20 to 30 minutes, until golden brown. Let cool 10 minutes before slicing and serving.
Store leftovers in zip-lock bag at room temperature. They freeze well, too.