Slice the pork on the diagonal into pieces or strips about ⅛ inch thick; it’s fine if the slices are not uniform in length or shape. In a medium bowl, toss the pork with 1 teaspoon oil, 2 teaspoons fish sauce and ¼ teaspoon salt.
In a 12-inch skillet over medium-high, heat the remaining 1 tablespoon oil until barely smoking. Add the pork in an even layer and cook, stirring just once or twice, until lightly browned but still pink in places, about 3 minutes. Add the curry paste and cook, stirring often, until any liquid released by the pork has evaporated and the paste begins to stick to the skillet, about 2 minutes.
Stir in the beans, broth, sugar and remaining 2 teaspoons fish sauce, then bring to a boil over high. Cook, stirring often, until the beans are tender-crisp and the pan is almost dry, about 5 minutes. Taste and season with salt. Transfer to a serving dish and sprinkle with the lime zest; serve with lime wedges.
