Prepare dry ingredients: In a large mixing bowl, combine 3 cups of All-Purpose Flour, 2 ½ teaspoon instant yeast, 3 tablespoon granulated sugar, 1 ¼ teaspoon salt, and ¼ cup potato flour (or ¾ cup dried potato flakes). Stir to combine.
Warm milk and butter: In a separate microwave-safe bowl or a saucepan, combine 3 tablespoon butter and 1 cup milk. Heat until the butter melts and the milk is warm (but not boiling). Let it cool slightly.
Form dough: Pour the warm milk mixture into the bowl with the dry ingredients. Add 1 large egg, and mix until a dough begins to form.
Knead dough: Transfer the dough to a floured surface and knead for about 8-10 minutes until smooth and elastic. Alternatively, use a stand mixer with a dough hook attachment.
First rise: Shape the dough into a ball and place it in a greased bowl. Cover with a damp cloth or plastic wrap, and let it rise in a warm spot for 1 to 1 ½ hours, or until doubled in size.
Shape rolls: After the dough has risen, punch it down to release any air. Divide the dough into 24 equal-sized pieces and shape each into a roll. Brush each piece with melted butter, then fold each piece in half (like a Parker House roll) or roll into a ball shape. Place the rolls into a greased 9x13-inch baking pan, ensuring the pieces are touching.
Second rise: Cover the shaped rolls with a clean cloth and let them rise again for 45 minutes to 1 hour, until they increase in size.
Preheat oven: Preheat your oven to 375°F (190°C).
Brush with butter and bake: Brush the risen rolls with melted butter using a pastry brush. Bake in the preheated oven for 15-20 minutes, or until golden brown on top.
Serve: Remove the rolls from the oven and brush them with more melted butter and sprinkle with flaky sea salt to taste. Let them cool slightly before serving.