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Step 1
Preheat oven to 350 degrees.
Step 2
Add butter and olive oil to a large oven proof pot with a lid (preferably a dutch oven) over medium high heat. Once melted, add onions, celery and carrot. Season lightly with salt and cook, stirring occasionally, until the vegetables are just browned. Add garlic and cook, stirring often, for an additional 2 minutes.
Step 3
Add the ham shank to the pot and pour in chicken stock. Season with black pepper and a pinch of salt. Bring to a low boil, cover and place in the oven. Bake at 350 degrees for 2-1/2 hours or until the meat is fork tender and falling off the bone.
Step 4
Remove pork from the pan and allow to cool for a few minutes. Meanwhile, strain the vegetables from the stock and return stock to pot. Add beans and rice and bring to a simmer. Taste for seasoning and add salt and pepper as needed. (Go easy on the salt, the ham has a LOT.)
Step 5
Remove ham from the bones and chop or shred with two forks. Place rice on 4 plates and top with equal amounts of chopped ham.
Step 6
Serve immediately.
Step 7
Share and Enjoy!