Preheat oven to 400 degrees F.
Use a paper towel to pat the pork dry and season with salt and pepper
Heat the butter and oil in a large cast-iron skillet over medium-high heat until simmering. Add pork and brown on all sides for about 8 to 10 minutes total and then transfer to a plate. Reduce heat to medium and add in pears, shallots, and thyme to the skillet. Cook, stirring occasionally until shallots and apples begin to soften, about 3 to 5 minutes.
Increase heat to high, stir in wine and simmer until liquid is reduced by half, about 1 to 2 minutes. Whisk in the cider and the mustard and bring to a boil. Add the pork back into the skillet, along with any juices on the plate.
Transfer the skillet to oven and cook until center of pork is 145 degrees, about 10 to 12 minutes.
Transfer pork to a plate to rest for 3 to 5 minutes and spoon apples, shallots, and sauce over the top, serve with sweet or mashed potatoes.