Step 1

Preheat the oven to 400 degrees F.

Step 2

Melt 1 stick of the butter in a small saucepan, then bring to a boil and cook until there are light brown specks in the butter, 3 to 4 minutes. Pour the browned butter into a small bowl and whisk in the sugar until dissolved. Whisk in the milk; the mixture should be lukewarm, around 110 degrees F. Next, whisk in the active dry yeast. Set aside until foamy, 5 minutes.

Step 3

In a large bowl, mix together the flour and salt. Make a well in the center, add the eggs and whisk the eggs together with a fork. Pour the browned butter mixture into the well. Using a fork, gradually incorporate the flour into the liquids. Continue stirring just until a shaggy dough comes together. Transfer to a lightly floured work surface and knead with floured hands until the dough becomes very smooth, about 5 minutes.

Step 4

Lightly grease a large bowl with olive oil. Add the dough, turning it once to coat. Cover with a clean kitchen towel and let rise until doubled in size, about 1 hour.

Step 5

Punch down the dough. Melt the remaining 1/2 stick of butter and use half of that to grease the bottom and sides of a 9-by-13-inch baking dish. Divide the dough into thirds and divide each third into 10 balls. To create smooth tops: roll each ball between your palms, and then stretch the dough across the top of the ball, pinching the excess at the bottom.

Step 6

Place the dough balls, seam-side down, in the prepared baking dish -- 5 to the short side, 6 to long side. Cover and let rise until slightly puffy, 30 minutes. Brush the tops with the remaining butter and sprinkle generously with flaky sea salt.

Step 7

Bake until the tops are golden brown and the rolls sound hollow when lightly tapped, 15 to 17 minutes. Serve warm.