For the stuffing: Melt the butter in a saute pan over medium heat. Add the onions, garlic and apples and cook, stirring occasionally, until softened, about 10 minutes. Season with salt and pepper and remove from heat.
In a large bowl, mix the breadcrumbs, cranberries, walnuts, parsley, sage and thyme. Add the chicken broth and the onion mixture; mix well and allow to cool down before adding the cheese. Season with salt and pepper. (The stuffing should be fairly dry, as the breadcrumbs will absorb juices from the pork while cooking.)
For the pork: Preheat the oven to 375 degrees F.
Trim the tenderloins of silverskin and excessive fat. Cut a slit down the length of the tenderloins to form a cavity for stuffing; sprinkle inside and out with salt and pepper.
Fill the cavity with the stuffing ¿ approximately 4 ounces per loin; do not overstuff. Tie the tenderloins with butcher's twine.
Heat the vegetable oil in a large pan over medium heat. Add the stuffed tenderloins; sear on all sides until golden brown. Transfer the pan to the oven and cook until the pork reaches an internal temperature of 150 degrees F, 15 to 20 minutes.
Remove from the oven; let rest for 7 to 10 minutes. Remove the butcher's twine and slice the pork into medallions. Serve with your favorite starch and vegetables.