Preheat oven to 275 degrees F, if using oven. If using slow cooker, don't turn on your oven.
In large dutch oven, heat olive oil over high heat.
Sprinkle salt and pepper over the pork tenderloins.
Add the pork tenderloins and sear each side until browned.
Remove from dutch oven and set aside.
Add onion (and more oil if needed) to pot and let cook until slightly softened, about 4-5 minutes.
Add garlic and thyme and cook another minute.
Add apple cider and broth to pot, scraping up any bits on the bottom, and then add pork tenderloins to the dutch oven. If using your slow cooker, place pork tenderloins in the slow cooker and pour liquid and onion mixture over it.
Cook on low for 6 hours in the slow cooker or place dutch oven in oven and cook 2 1/2 - 3 hours, until meat is fork tender.
Remove meat from liquid and set aside, tenting it with foil to keep it warm.
Pour remaining liquid through a strainer into saucepan.
Add dijon mustard and bring to a boil.
Simmer over medium heat, stirring often, until slightly reduced about 10 minutes.
Pour over shredded meat.