Make the dough: In the bowl of a stand mixer fitted with the dough hook, combine the milk and yeast and let stand until foamy, about 10 minutes. With a fork, stir in the butter, sugar, salt and egg. With the mixer on low, add the flour and then the herbs. Increase the speed to medium and knead the dough until it is smooth and elastic, about 5 minutes.
Lightly butter a large bowl. Transfer the dough to the bowl, then cover and set in a warm place until doubled in size, 1 to 4 hours, depending on the temperature of your house.
Butter a 13-by-9-inch baking pan. Transfer the dough to a work surface and cut into 18 equal pieces. Roll each piece into a tight ball. Transfer the dough balls to the prepared pan, spacing them evenly (rolls will touch once they have risen). Cover and set in a warm place until doubled in size, about 1 hour.
Finish the rolls: Preheat the oven to 400 degrees F. Very gently brush the rolls with some melted butter and sprinkle with some flaky sea salt. Bake until golden, 15 to 18 minutes. Brush with more melted butter and serve warm.