Remove the ends from the beans. Snap the beans in 2 pieces, place into a colander, wash, and set aside to drain.
Meanwhile, in a large cast iron Dutch oven, lightly brown the salt pork in the bacon grease over medium heat, turning often, for approximately 10 minutes. Toss the green beans into the pot, stirring them with a wooden spoon to coat well with the pork fat. Add the broth and House Seasoning. Cook over medium-low heat, covered tightly, for approximately 30 minutes, or until the beans are half done.
While the beans are cooking, peel a center strip from each new potato with a potato peeler. At the end of 30 minutes, add the potatoes and onion to the beans; add 1/4 cup more broth, if needed. Cook, covered tightly, until the potatoes are tender, approximately 25 to 30 minutes, periodically checking the pot to make sure a small amount of liquid remains. When the potatoes are tender, tilt the lid slightly, off to the side of the pot, and continue to cook until the green beans are wilted, approximately 15 minutes. While cooking, add the butter and season with pepper.
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