Special equipment: an instant-read or candy thermometer
Preheat the oven to 400 degrees F. Grease a rimmed baking sheet with cooking spray.
Microwave the potatoes until tender, about 10 minutes, depending on your microwave. Slice the potatoes in half, spoon out the flesh and mash slightly. Measure out 1 cup of the potatoes and reserve.
Warm the milk in a small saucepan to 90 degrees F. Activate the yeast by sprinkling it over the warm milk. Let stand for 5 minutes.
In the bowl of a stand mixer fitted with the dough hook, combine the coconut oil, sugar, salt, egg and reserved 1 cup mashed potatoes and mix until smooth, about 1 minute. Add the yeast mixture. Add the flour in 2 batches and mix after each addition, until the dough starts to pull from the sides and looks elastic, 2 to 4 minutes.
Turn the dough out onto a floured surface and knead gently until smooth and supple, about 1 minute. Divide the dough into 16 portions (about 2 ounces each) and roll each into a ball on your work surface to create a roll. Place on the prepared baking sheet. Let the rolls rest until doubled in size, about 15 minutes.
Brush the rolls generously with the melted butter and sprinkle with the sea salt. Bake until the tops are golden brown, 13 to 15 minutes.