Special equipment: an instant-read or candy thermometer
Preheat the oven to 400 degrees F. Grease a baking sheet with cooking spray.
Microwave the potatoes until tender, about 10 minutes depending on your microwave. Slice in half, spoon out the innards of the potatoes 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 a dough hook, combine the coconut oil, sugar, salt, egg and reserved 1 cup mashed potatoes and beat until smooth, about 1 minute. Add the yeast mixture to the potato mixture. Add the flour in 2 parts and mix 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 portion into a ball on your work surface to create a roll. Place on the prepared baking sheet. Allow the rolls to rest until doubled in size, about 15 minutes.
Brush generously with melted butter and sprinkle with the sea salt. Bake until the tops are golden brown, 13 to 15 minutes.