Mix broth, lime juice, soy sauce, and Sriracha in a measuring cup. Cut eggplant into lengthwise batons about 1/2 in. thick and 3 in. long.
Cook pork in a 12-in. frying pan or wok over high heat, stirring to break up clumps, until lightly browned, 4 to 6 minutes. Add about 2 tbsp. broth mixture and stir until liquid evaporates, 1 minute. Transfer to a bowl and wipe out pan.
Return pan to high heat and add 2 tbsp. oil. When hot, add eggplant and cook, stirring occasionally, until beginning to brown, 3 minutes. Add shallots, remaining 1 tbsp. oil, and 1/4 cup water and continue to stir-fry until eggplant is browned and tender and shallots are caramelized, 7 to 9 minutes more; add a little more water if pan juices start to darken too much.
Pour in remaining broth mixture and pork and stir until most of liquid is absorbed, 1 to 2 minutes. Transfer to a serving dish and toss with cilantro.