In a large bowl whisk together the melted butter, eggs, yolks, milk, and salt. Be sure you allow the butter to cool before incorporating it, or else it may cause your eggs to curdle (as it will begin to cook the eggs if too hot).
Cut up the loaf of bread into small cubes. Place about half the cubes in a well-buttered casserole dish.
Pour half the egg mixture over the bread. Toss in the sun-dried tomatoes, half of the rosemary, and 1 cup of the cheese. Add the remaining bread cubes over this. Pour on the remaining egg mixture. Use your clean hands to press the bread cubes down, just enough so that all the bread gets soaked in the egg mixture. Top with the remaining cheese, a little pepper, and the remaining rosemary.
Bake at 350°F for 28-30 minutes. Allow to cool for 5-8 minutes before cutting into the casserole.