Cook rice according to package instructions. Heat about 1/2 in. oil in a large frying pan over medium-high heat until oil begins to ripple. Fry wrappers, one at a time, until golden on both sides, about 1 minute per side. Drain wrappers on paper towels.
Carefully drain all but 2 tbsp. oil from pan, add garlic and ginger, and cook until fragrant and softened, 30 seconds to 1 minute. Add pork and fish sauce, and cook until pork is brown and crisp at the edges, 5 to 7 minutes, breaking up pieces with a wooden spoon.
Whisk together lime juice and soy sauce in a small bowl. In a large bowl, toss cabbage, carrots, and chopped cilantro with 1 tbsp. soy sauce mixture.
Divide crisp egg roll wrappers among 4 plates. Top each with rice and pork. Mound carrot-cabbage slaw on pork and sprinkle with a few cilantro leaves. Serve with remaining soy sauce mixture for drizzling.