Add milk, 8 tablespoons of unsalted butter, sugar, and salt to a small sauce pan and scald over medium heat. Scald means to heat right before a simmer. You should see small bubbles form around the edges of the pan. Remove from heat and let cool.
Attach bowl to stand mixer and fit mixer with dough hook. Add flour and yeast and mix on low to combine. Add in egg and mix on low. With the mixer still on low, slowly drizzle in melted butter and milk mixture, making sure all sugar makes it into the flour. Once it's all poured in, let the dough hook mix everything together until the dough forms.
Once dough forms, turn up speed to medium and knead dough for 8 minutes. If the dough is still sticking to the sides after 8 minutes, add flour a tablespoon at a time until it loosens up. Place dough ball in a greased bowl and cover with a towel. Let it rise for 1½ hours. It should be double in size. Grease two square pans (9x9 or 8x8). Set aside.
Punch down risen dough and remove from bowl. Place on clean counter with a little sprinkled flour. Cut dough into 4 even slices. Working with one piece at a time, roll into a 12x6 inch rectangle, trimming uneven sides before measuring. Brush rectangle of dough with melted butter. Cut the rectangle into 3 strips measuring 4x6 inches. Then, cut each strip into three 4x2 inch rectangles. Take each rectangle and roll into a log. Place the log into one greased pan. Repeat with the rest of the rectangles and then start again with another piece of dough. Continue until all 36 logs are formed and in the greased pans.
Cover pans with a towel and let them rise again for 1½ hours. At the 30-minute mark, preheat oven to 350 degrees. **If using a metal pan, preheat to 325 degrees**
Remove towel from rolls and brush with more melted butter. Bake in preheated oven for 28-30 minutes, or until deep brown on top. Remove from oven and immediately brush with melted butter and sprinkle with flaky sea salt.