Rub pork chops with salt and pepper. In a heavy skillet, melt 2 tablespoons of the butter over medium-high heat. Add pork and cook 3 to 4 minutes or until browned on first side. Turn pork and reduce heat to medium. Cook 2 to 3 minutes longer or until pork is no longer pink in center (at least 145°F). Note that longer cooking times may be required for bone-in pork chops. Transfer to plate; cover with foil to keep warm.
In same skillet, melt remaining 1 tablespoon butter over medium-high heat; add pineapple, and cook 2 to 4 minutes, turning once, until pineapple is golden brown on edges.
Remove from heat; add rum, and return to heat; cook 1 to 2 minutes over medium-high heat until rum absorbs into mixture. Add sugar; cook 1 to 2 minutes or until sugar melts and begins to caramelize.
Pour pineapple mixture over pork. Sprinkle with mint. Serve with lime wedges and rice.
We substituted sweet plantains as a side dish, instead of the rice. Yum!