Combine ingredients for the egg/cream mixture and whisk until smooth. Break croissants into smaller pieces (halves if they are smaller, and thirds if they are bigger).
Soak the croissant halves in ¾ of the egg/milk mixture, setting ¼ of it aside. Butter or spray a baking dish and add the croissant pieces to it.
Preheat oven to 350 degrees. Thinly slice ham and cut into bite sized pieces. Tuck cubes of cheese and slices of ham between the croissants. Pour the remaining ¼ egg/cream mixture over the top. Cover and bake for 30 minutes.
Meanwhile make the rosemary butter but melting butter in a skillet with a few sprigs of rosemary. Cook for a few minutes on low and then discard the rosemary.
Brush bake with rosemary butter and bake for about 20 min or so. Crank oven up to broil for last 3-4 minutes to get the top nice and bubbly. Enjoy!