In a small pan, melt 1/2 cup of the butter over medium heat. Add the milk and sugar and stir to combine. Using a thermometer, check the temperature of the butter and milk mixture; when it's 105 degrees F, remove from the heat. Add the yeast and stir to dissolve. Let the yeast bloom for about 5 minutes, until the mixture is bubbly. If mixture doesn't bubble and smell "yeasty," throw it out and start over.
Pour the yeast mixture into the bowl of a stand mixer fitted with the dough hook. Add 4 cups of flour. Turn the mixer to low and knead until just combined, about 1 minute. Add the egg, 1 1/2 tablespoons of the chopped herbs, half of the garlic, and the kosher salt, and continue kneading on low speed until soft and smooth, tacky but not sticky, adding the remaining 1/4 cup flour if the dough is too wet.
On a lightly floured surface, shape the dough into a ball and place it in a large greased bowl. Cover with plastic wrap and let the dough rise in a warm, draft-free area for about 1 1/2 hours, until doubled in size.
Remove the plastic wrap and gently punch down the dough. Cut the dough into 4 equal pieces, then shape into small balls about 2 ounces each for 18 dough balls in total.
Butter a large cast-iron roasting pan or baking dish and place the shaped dough into the dish. Let the dough rise for 30 minutes. While the dough is rising, preheat the oven to 350 degrees F.
Bake the rolls for 25 to 30 minutes, or until golden brown.
In a small pan or in the microwave, melt the remaining 1/4 cup butter with the remaining garlic. Gently brush the dough with the melted garlic butter, top with remaining herbs, and sprinkle with flaky sea salt. Serve warm.