Combine plums, chicken broth, minced onion, balsamic vinegar, and brown sugar in a small saucepan. Bring to a boil and reduce to a simmer. Allow it to simmer for 20 minutes or until the sauce is thickened and reduced by almost half. The plums should break down on their own, but feel free to mash them a little with the back of a spoon.
Preheat oven to 425 degrees.
Prep the pork tenderloins. Rub the meat down evenly with salt, pepper, and dry mustard.
Heat a large skillet over medium high heat and add the olive oil. Add the pork to the pan and brown on all sides (about 7 minutes total).
Transfer the browned pork to a baking pan lined with foil and brush evenly with the plum sauce (about 1/2 a cup).
Bake for 15 minutes and remove pork from the oven. Turn the tenderloins over and brush with additional plum sauce. Cook for 10 more minutes or until a thermometer inserted into the thickest part of the meat registers 145 degrees.
Transfer the meat to a platter, cover loosely with aluminum foil, and let rest for 10 minutes.
Slice into medallions and serve with extra plum sauce.