HPK fat (Heart/Pancreas/Kidneys) is the realllllly good stuff that you make your cooking fats out of. That's the type of fat you're after. Not sure if it's too "offal" for you, but lamb tongue is quite the delicacy. Ask to receive ALL bones (save the head if you're squeamish) , this will provide you with plenty of stock!
"You can demonstrate the purpose and limits of human digestion with a simple experiment: eat a steak with some whole corn kernels, and see what comes out the other end. It won’t be the steak."