In a small saucepan, gently heat the whole milk and 1/4 cup of the unsalted butter until warm but not boiling. Remove from heat and stir in the sugar and active dry yeast. Let it sit for about 5-10 minutes until it becomes frothy.
In a large mixing bowl, combine 4 cups of all-purpose flour and kosher salt. Make a well in the center and add the yeast mixture along with the egg.
Stir in the minced garlic and chopped fresh herbs. If the dough seems too sticky, gradually add more flour, a tablespoon at a time, until it comes together.
On a floured surface, knead the dough for about 8-10 minutes until it is smooth and elastic. If using a stand mixer, knead on medium speed using a dough hook for about 5-7 minutes.
Grease a large bowl with a little bit of the leftover melted butter. Place the dough in the bowl, cover with a kitchen towel, and let it rise in a warm area until it doubles in size, about 1-2 hours.
Punch down the dough to release the air. Turn it out onto a floured surface and divide the dough into 12 equal pieces. Shape each piece into a ball and place them on a baking sheet lined with parchment paper, leaving space between each roll.
Cover the rolls with a kitchen towel and let them rise for another 30-45 minutes until puffy.
Preheat your oven to 375°F (190°C).
Before baking, brush the tops of the rolls with melted butter and sprinkle with flaky sea salt. Bake for 15-20 minutes or until golden brown.
Remove the rolls from the oven and let them cool on a wire rack. Serve warm and enjoy the deliciousness of your Garlic Herb Parker House Rolls!