In a large skillet, heat 1 tbsp. oil over medium. Add the chicken, chopped onion, paprika, and 1 tsp. salt. Cook, stirring occasionally and breaking up with a spoon, until the chicken is lightly browned and cooked through, about 5 minutes.
In a small bowl, whisk the remaining 2 tbsp. oil, the lime zest and juice, fish sauce, and brown sugar. Stir into the chicken mixture. Divide among the whole cabbage leaves. Top with the sliced onion and cabbage, the herbs, and chile. Serve with lime wedges.