In the bowl of a stand mixer with the dough hook attached, stir together 3/4 cup flour, yeast, sugar, and salt. When you're measuring the flour, DO NOT scoop up the flour with the measuring cup and level it off like that. Use a spoon to fluff up the flour first, then sprinkle the flour into the cup with the spoon. Then you can go ahead and level it off with a knife before dumping it into the bowl.
In a separate small bowl, mix milk, butter, and water. Microwave 15 seconds at a time until liquid is very hot, but not scalding - about 120 - 130 degrees. I never use a thermometer, I just test it with my finger. The butter won't be completely melted just yet. Dump this into the mixer bowl and turn on medium speed, scraping the sides, until you have very wet dough.
Next, add an additional 1 1/4 - 1 3/4 cup flour (using the same sprinkle method above) until the dough cleans the sides of the bowl and it comes together in a ball. Keep your mixer on medium speed and set the timer for 8 minutes - this is called kneading. God bless my stand mixer! Transfer dough to a separate bowl, cover with plastic wrap, and allow to rest 10 minutes.
Cut dough into 12 equal (ish) balls and place in a greased square baking dish. Cover and set in a warm place (my stove top with the hood light on does the trick) for 30 minutes or until doubled in size.
Brush tops of risen rolls with beaten egg (you won't need all of it). Then stir together remaining topping ingredients (except butter) and sprinkle over the tops of the rolls, pressing in the tops as needed.
Bake at 375 for 20 minutes or until tops are golden brown. Drizzle tops with melted butter and allow rolls to cool 10 minutes before serving.