Dissolve yeast in the warm water, about 10 minutes.
Combine 4 Tbsp. butter, salt and sugar in a large bowl.
Warm the milk gently in a small saucepan over medium heat. Stir the warm milk into the butter mixture.
Whisk in the yeast mixture and egg. Then stir in the flour.
Dump the dough onto a lightly floured surface and knead 7-8 minutes until a soft dough forms. (Alternatively, knead the dough in the bowl of a stand mixer fitted with a dough hook attachment on low speed).
Place dough into an oiled bowl. Cover with a wet dish towel and let the dough rise in a warm place until it doubles in size, about 90-120 minutes.
Punch the dough down and dump it back onto a lightly floured work surface. Roll dough out into a rectangle measuring 13"x15". Melt 4 Tbsp. butter and brush it onto the dough. (There should be some butter left over for finishing)
Divide dough in half, cutting down the middle crosswise, so there are two smaller rectangles. Roll each rectangle from long end to long end, jelly roll style. Cut 10 equal pieces in each rectangle, for a total of 20 pieces.
Use the remaining 2 Tbsp. of butter to coat the bottom and sides of a 9x13 baking dish. Arrange the rolls in 5 rows of 4, leaving 1/2" of space between each roll. Cover with a dish towel. Let rise 45-60 minutes. (the rolls will expand slightly, but will not double in size)
Preheat the oven to 350 degrees. Bake 20-25 minutes, until puffed and golden. Brush with remaining melted butter and sprinkle generously with sea salt.