In the bowl of a stand mixer with a bread hook, combine warmed water, sugar, and yeast. Let stand for 5-10 minutes until foamy.

Melt 2 tablespoons of the butter and combine it with lukewarm milk. Add the milk mixture to the yeast in the stand mixer, along with the lightly whisked egg, and stir to combine. Add the salt and flour, mixing on medium speed until the dough is formed into a ball.

Lightly grease a large bowl and transfer the dough to it. Cover the bowl with a tea towel and let the dough rise in a warm area for 1 hour.

Once the dough has risen, dump onto a well-floured surface and knead for 2-3 minutes.

Weigh the dough and divide it into 8 sections. Shape each section into a ball.

Place the balls seam side down on a cast-iron skillet or greased pan. Cover with a tea towel and let rise for another hour.

Preheat the oven to 375°F after the rolls have risen for 30 minutes.

Remove the tea towel and bake for 20-25 minutes until golden brown and the internal temperature reaches 200-205°F.

Prepare the garlic herb butter by melting the remaining 2 tablespoons of butter with the garlic and herbs. Set aside.

Brush the butter mixture on top of the hot rolls, sprinkle with flakey sea salt, let rest for about 10 minutes, and serve warm.