Heat oven to 400 degrees F. Rub pork with 1 teaspoon honey and 1/4 teaspoon each salt and pepper; place in a roasting pan. Roast at 400 degrees F for 25 to 30 minutes, turning halfway through, or until internal temperature registers 155 degrees F on an instant-read thermometer.
Meanwhile, heat oil in a large nonstick skillet over medium-high heat. Add cabbage and cook, covered, for 6 minutes. Reduce heat to medium; stir in remaining 2 teaspoons honey, apple, caraway seeds and remaining 1/4 teaspoon each salt and pepper. Cook for 6 minutes, uncovered, stirring, until cabbage is tender.
Cut pork into 1-inch slices and serve with slaw.