Preheat oven to 400 degrees F. Sprinkle all sides of pork with salt and pepper. Heat large cast iron or other heavy skillet over medium-high heat. Add vegetable oil to skillet. Transfer pork to skillet; sear 8 to 10 minutes or until browned on all sides, turning every 2 minutes.
Transfer skillet to oven; cook 15 to 17 minutes or until internal temperature of pork reaches 145 degrees F. Transfer pork to cutting board; let stand 5 minutes before slicing.
Meanwhile, in medium saucepot, cook apples, vinegar, water, mustard, chili powder and cayenne over medium-high heat 18 to 20 minutes or until apples are softened and most liquid is absorbed, stirring occasionally. Use spoon to lightly mash and break up apples as they cook.
Thinly slice pork and build sliders using pork, apple compote and arugula.
This website provides estimated nutrition information as a courtesy only. You should calculate the nutritional information with the actual ingredients used in your recipe using your preferred nutrition calculator.