Line a 9x13” baking pan with parchment paper, set aside.
Add sugar, water and yeast to the bowl of your standing mixer fitted with the dough hook. Let the mixture sit for 5-10 minutes until foamy.
Melt butter completely. Mix in milk and warm the mixture in the microwave or on the stovetop until it’s combined and not lumpy (but just slightly warm). Set aside to cool comepletely!
Once yeast is foamy (proofed) and butter/milk is cool, pour butter/milk mixture into the bowl of your standing mixer. Mix on low-speed until combined.
Add egg and mix until combined.
Add 3 cups of flour and ½ TBS salt and knead with dough hook. Add more flour a little bit at a time until a slightly-sticky ball forms.
Grease a large bowl and transfer dough to the bowl. Cover with a damp cloth and set in a warm place to rise for about 1 hour, or until doubled in size.
Once dough has doubled, flour your hands and squeeze it to remove the gas.
With floured hands, form 12, equally-sized dough balls.
Roll them until they’re smooth balls.
Place them into your prepared baking sheet evenly spaced into 4 rows of 3.
Cover with a damp towel and let rise in a warm place until doubled in size (about 30-60 minutes).
When you notice your rolls have risen about halfway, Preheat your oven to 375 degrees F.
Place fully-risen rolls into preheated oven and bake for 25-30 minutes, until the rolls are golden-brown on the top and sound hollow when tapped with a wooden spoon.
Remove rolls from oven and immediately brush them with melted butter and sprinkle with sea salt.