Place the tenderloins on a sheet pan and pat them dry with paper towels. Combine the rosemary, thyme, 1 tablespoon salt, and 1 teaspoon pepper in a small bowl. Rub the tenderloins all over with 2 tablespoons of olive oil. Sprinkle all sides with the herb mixture. If there is a thinner "tail," fold it underneath so the tenderloin is an even thickness throughout. Wrap the tenderloins completely with a single layer of prosciutto. (I place the prosciutto sideways with the ends wrapping under the tenderloins.) Tie in several places with kitchen string to hold the prosciutto and the "tail" in place.
Roast for 20 to 25 minutes, until an instant-read thermometer inserted in the middle of the end of the tenderloin reads 140 degrees F for medium rare and 145 degrees F for medium. Cover the tenderloins tightly with aluminum foil and allow to rest at room temperature for 15 minutes. Slice diagonally in thick slices and serve warm with apple chutney.