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1
In the bowl of a stand mixer, or in a large bowl, in the order provided, add 1/4 cup + 1/2 tbsp butter (melted and cooled), then 1 egg and 1 egg yolk, followed by the milk, mashed potatoes, sugar, 1 1/4 tsp salt, flour and yeast. Start combining all ingredients before using the stand mixer; then using stand mixer and the dough hook attachment, combine all ingredients to form a homogeneous dough. Let rest for 10 minutes, then continue with the dough hook attachment till it passes windowpane test.
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2
The windownpane test entails taking a walnut size amount of the dough or a small area of the dough and stretch it. You want it to stretch into a thin film that does not break easily. If you are able to do that, you have passed the windowpane test and it means that you have sufficiently kneaded the dough. Refer to this link to see a picture of a dough that has passed this test, http://www.thekitchn.com/bakers-techniques-how-to-do-th-70784.
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3
Place dough into a lightly oiled/greased bowl; also lightly brush a tiny bit of oil on top of the dough, and cover the top of the bowl with plastic wrap. Set aside until it doubles in size. You can like me boil 2 cups of water in the microwave, and place the bowl with the dough next to the boiled water. Close microwave, unplug, and let dough rise till doubled. Be patient. It may take a couple of hours or more depending on the temperature in the air that surrounds the bowl.
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4
Once dough has doubled, turn dough onto a clean work surface (you can lightly oil it but I usually don't see the need), and portion dough into 18 balls. Place onto a lightly oiled parchment lined baking sheet in 6 rows of 3 rolls each. Very lightly brush the top of the rolls with oil and gently cover with a layer of plastic wrap. Set in a warm place until doubled in size, one hour or more. The baking sheet is too big for the microwave trick.
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5
When the rolls are almost ready, heat the oven to 375 degrees. Carefully melt in a saucepan or in microwave the remaining 2 tbsp of butter, let cool a bit and then stir the remaining yolk. Gently brush the tops of the risen rolls with the butter mixture, then sprinkle the remaining 1/2 teaspoon coarse sea salt.
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6
Bake the rolls until golden brown and completely set, about 20 minutes. Remove and cool slightly before serving. I prefer to wait about 30 minutes.
