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Flour mixture: In a large bowl, whisk together the flour, yeast, salt, and sugar.
Potato mixture: In a separate bowl or measuring jug, whisk together the mashed potato, warm milk, and melted butter until mostly smooth.
Combine: Pour the potato mixture into the flour mixture. Stir with a spatula or dough whisk until a soft, sticky dough forms.
First rise: Cover the bowl and let the dough rise for 50–60 minutes, or until puffed and about doubled in size.
Lightly flour your work surface. Turn the dough out onto the floured surface and lightly dust the top with flour.
Roll the dough into a rectangle about 10 x 12 inches (24 x 30 cm).
Cut the dough into 4 strips from the short side, each about 2½ inches (6 cm) wide.
Cut 5 rows in the other direction, about 2½ inches (6 cm) apart, to create 20 square pieces.
Transfer the squares to a lined baking tray, leaving about 1 inch (2.5 cm) between them.
Second rise: Cover loosely and let rise for 20–25 minutes, or until slightly puffed.
Bake at 350°F (180°C / 160°C fan) for 17–20 minutes, rotating the tray halfway through baking, until lightly golden.
Garlic butter: While the rolls bake, stir together the melted butter, garlic powder (or grated garlic), parsley, and salt if using.
Brush the garlic butter over the hot rolls as soon as they come out of the oven.