In a large mixing bowl or the bowl of a stand mixer fitted with the dough hook attachment, combine the mashed potatoes, melted butter, sugar, and beaten eggs.
Add the yeast mixture to the bowl and mix until well combined.
Gradually add the flour and salt to the wet ingredients, mixing until a soft dough forms.
Turn the dough out onto a floured surface and knead it for about 5-7 minutes, adding more flour as needed, until the dough is smooth and elastic.
Place the dough in a greased bowl, turning once to coat, and cover it with a clean kitchen towel or plastic wrap. Let it rise in a warm, draft-free place for about 1-1.5 hours, or until doubled in size.
Once the dough has risen, punch it down to release any air bubbles. Turn it out onto a lightly floured surface and divide it into 16 equal pieces.
Shape each piece of dough into a smooth ball and place it in a greased 9×13-inch baking dish, spacing them evenly apart.
Cover the baking dish with a clean kitchen towel or plastic wrap and let the rolls rise for another 30-45 minutes, or until they have doubled in size.
Preheat your oven to 375°F (190°C).
Bake the rolls in the preheated oven for 20-25 minutes, or until they are golden brown on top and sound hollow when tapped on the bottom.
Optional: Brush the warm rolls with melted butter and sprinkle them with flaky sea salt for extra flavor.
Let the rolls cool slightly before serving.
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