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Heat 1 tbsp olive oil in a pan over medium high heat.
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Season the pork tenderloin on all sides with salt, pepper and Italian seasonings. Cut the pork tenderloins in half if needed to fit in your slow cooker.
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Sear the pork for 5-6 minutes per sides, or until golden brown.
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Place the pork in a slow cooker.
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In a small bowl, mix together the chicken broth, soy sauce, balsamic vinegar, brown sugar and garlic.
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Pour the sauce over the pork. Cover the slow cooker and cook on LOW for 6-8 hours, or HIGH for 4 hours.
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Remove the pork from the slow cooker and place on a plate; cover with foil to keep warm.
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Pour the liquid from the slow cooker into a pot. Heat the pot over medium heat and bring the sauce to a simmer.
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Mix the cornstarch with ¼ cup cold water. Add the cornstarch to the pot and bring to a boil.
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Cook for 1 minute, or until sauce has just thickened.
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Add the butter to the pot and stir until melted. Remove the pot from the heat.
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Slice or shred the pork and pour the sauce over the top. Sprinkle with parsley and serve.