Warm the milk in a small saucepan over low heat until it reaches 110 degrees F on a thermometer. It should feel warm on your wrist but not hot. Pour it into the bowl of a stand mixer or a large mixing bowl. Sprinkle the yeast and one tablespoon of the sugar over the milk and stir gently. Let it sit for 5 to 8 minutes until it looks foamy and slightly puffy on top. If nothing happens, your yeast may be old and you should start again with a fresh packet.

Add the eggs, softened butter, remaining 2 tablespoons of sugar, and fine salt to the yeast mixture. Mix briefly to combine. Add the flour all at once. If using a stand mixer, knead with the dough hook on medium speed for 7 to 8 minutes until the dough is smooth, slightly tacky, and pulls cleanly away from the sides of the bowl. If kneading by hand, work the dough on a lightly floured surface for 10 minutes. The dough should feel soft and elastic, not stiff.

Shape the dough into a ball and place it in a lightly greased bowl. Cover with a clean kitchen towel or plastic wrap and set it in a warm spot to rise until doubled in size, about 1 hour. A turned-off oven with just the light on works great.

Brush a 9x13 inch baking pan generously with the melted butter. Punch the risen dough down and turn it out onto a lightly floured surface. Divide it into 18 equal pieces, roughly the size of a golf ball each. Roll each piece into an oval about 4 inches long, brush the center lightly with melted butter, then fold one long side over to meet the other, like closing a small book. Place each folded roll seam-side down in the prepared pan in three rows of six. They should be touching or nearly touching.

Cover the pan loosely with plastic wrap and let the rolls rise again for 45 minutes at room temperature, until they are puffed, touching each other, and look pillowy. While they rise, preheat your oven to 375 degrees F.

Brush the tops of the risen rolls with a thin coat of melted butter. Bake for 18 to 22 minutes, until the tops are deep golden brown and the rolls sound slightly hollow when tapped. The internal temperature should read around 190 degrees F if you want to check.

While the rolls bake, stir together the softened 4 tablespoons of butter and the minced chives in a small bowl until well combined. The moment the rolls come out of the oven, brush them generously with the chive butter so it soaks into the hot surface. Immediately sprinkle the tops with flaky sea salt. Serve warm directly from the pan.