In a large mixing bowl, combine the flour, instant yeast, granulated sugar, and salt. Use a whisk to ensure everything is evenly mixed.
In a small saucepan, gently heat the milk, water, and butter over low heat until the butter melts and the mixture is warm but not hot (about 110°F or 43°C). Remove from heat.
Add the potato flakes to the dry ingredients, followed by the warm milk mixture. Stir with a wooden spoon or spatula until the dough starts to come together.
In a small bowl, beat the large egg. Add it to the dough and mix until fully incorporated.
Transfer the dough to a lightly floured surface. Knead for about 5-7 minutes until the dough is smooth and elastic. If the dough is too sticky, gradually add more flour, one tablespoon at a time, until it reaches the right consistency.
Place the kneaded dough in a lightly greased bowl. Cover it with a kitchen towel and let it rise in a warm place for about 1 hour, or until it has doubled in size.
Once the dough has risen, punch it down to release the air. Divide the dough into 12 equal pieces. Shape each piece into a ball and place them on a baking sheet lined with parchment paper. Leave some space between each roll.
Cover the rolls with a towel and let them rise for another 30-45 minutes, until they have puffed up.
Preheat your oven to 375°F (190°C). Once the rolls have risen, bake them for 15-20 minutes, or until they are golden brown on top.
Remove the rolls from the oven and let them cool on a wire rack. Serve warm with butter or your favorite spread.