Toss the pork with the curry powder, 1 teaspoon brown sugar, the lime zest and a generous pinch each of salt and pepper in a large bowl; set aside. Put the potatoes in a 6- to 7-quart slow cooker and top with the cilantro stems and half of the red onion slices.
Whisk the coconut milk with 1/4 cup water and the curry paste in a small bowl. Pour into the slow cooker. Add the pork and nestle into the vegetables and sauce. Cover and cook on low, 7 hours.
Transfer the pork to a cutting board; let rest. Stir the green beans into the slow cooker and let stand, uncovered, 10 minutes. Toss the remaining red onion with the lime juice in a small bowl and let stand 10 minutes. Stir the remaining 1 teaspoon brown sugar into the curry sauce and season with salt and pepper.
Divide the green beans, potatoes and sauce among bowls. Slice the pork and add to the bowls. Top each serving with the onion and any remaining lime juice in the bowl, the bean sprouts and cilantro leaves. Serve with lime wedges.