Preheat the oven to 350°F, positioning a rack in the center. Trim the pork tenderloin by removing the silverskin with a sharp knife. Pat dry thoroughly with paper towels.

In a small mixing bowl, blend together the brown sugar, kosher salt, paprika, and cayenne pepper. Rub this seasoning mixture uniformly over the surface of the tenderloin. Encase the pork with bacon slices, securing them with toothpicks along the sides.

Warm the oil in a large cast iron or oven-safe skillet over medium-high heat until it shimmers. Place the bacon-wrapped tenderloin into the skillet and sear without disturbing it for 6 to 8 minutes until a rich brown crust forms. Turn the tenderloin and sear the opposite side similarly.

Combine the chutney with the mustard in a separate bowl and liberally brush this glaze over the top of the tenderloin. Transfer the skillet to the preheated oven and roast until the internal temperature of the pork reaches 140°F, approximately 10 to 14 minutes.

Withdraw the skillet from the oven, tent the pork loosely with aluminum foil, and allow it to rest for 10 to 15 minutes so the juices settle and the pork finishes cooking gently. Discard toothpicks and slice the tenderloin into 1/4- to 1/2-inch thick medallions. Accompany with remaining chutney if desired.