Place ham in a large roasting pan, cut-side down. Press brown sugar evenly onto ham. Pour apple into roasting pan and cover with a lid or aluminum foil.
Bake in the preheated oven until ham is heated through, about 80 minutes. An instant-read thermometer inserted into the center should read 160 degrees F (70 degrees C). Let ham rest for 10 minutes before transferring to a serving plate. Pour remaining pan juices into a saucepan.
Combine flour and milk in a jar with a lid; shake until mixture is blended.
Bring pan juices to a boil. Slowly whisk flour mixture into the saucepan until gravy is thick, about 5 minutes.
