In a small sauce pot, combine milk, butter, and sugar. Set over medium heat. Cook until butter has melted. Stir often to ensure milk does not burn on the bottom or sides of pan. Remove from heat and pour into the bowl of a stand mixer. Let sit until liquid has cooled to a temperature of 120 degrees F.
Once liquid has cooled, whisk in yeast. Let stand for 5-7 minutes until mixture is fragrant. Attach paddle to mixer. Add eggs. Mix on low speed until combined.
Add 2 cups of flour. Continue mixing on low speed. Add another 2 cups flour, along with sea salt. Continue mixing on low speed. Scrape down bowl as needed to ensure thorough mixing.
Remove paddle attachment and switch to dough hook attachment. Add remaining 2 1/2 cups of flour. Knead on low speed until flour has been incorporated. Increase speed to medium and knead dough for 3-5 minutes until smooth. Dough will be a bit tacky. Do not be tempted to add additional flour. Continue to knead until dough can easily be scraped off the sides of the bowl.
Place dough inside a greased bowl. Cover with plastic wrap. Cover with dish towel and allow to rest at room temperature for 30 minutes.
Remove cover. Transfer dough to a lightly floured work surface. Divide dough into 24 equal parts. Roll into 24 balls and place on a parchment lined baking sheet* (18x13-inch).
Cover with plastic wrap and allow to rest for another 30 minutes.
Preheat oven to 350 degrees F. Uncover dough, it should have slightly risen during this time. Make egg wash by whisking together egg and water. Brush egg wash over bread rolls. Bake for 20-25 minutes until bread is golden brown on top and has an internal temperature of at least 190 degrees F. Allow to slightly cool in pan.
Right before serving, brush bread rolls with melted butter and sprinkle sea flakes on top. Serve bread warm.