Sprinkle pork with with salt and black pepper. In a large skillet brown pork, one-third at a time, in hot oil over medium-high heat. Add more oil as needed during cooking. Place meat in a 4- to 5-quart slow cooker.
Add the next four ingredients (through ginger) to pork in cooker. Stir together broth and curry paste; stir into mixture in cooker.
Cover and cook on low for 5 hours or on high for 2 1/2 hours. If using low, turn cooker to high. Stir in sweet pepper. Cover and cook 30 minutes more.
Stir coconut milk and lime juice into cooker. Serve curry over rice with lime wedges and topped with basil.