Add butter and oil to pan; swirl until butter melts.
Add cabbage, apple, caraway seeds, and salt; cover and cook 5 minutes. Uncover and cook 5 minutes or until cabbage and apples are tender, stirring occasionally.
Heat a large skillet over medium-high heat.
Add 1 tablespoon canola oil; swirl to coat.
Add 2 cups sliced onion; saut 2 minutes.
Add 8 cups sliced green cabbage, 1 cup hard cider or regular cider, 2 tablespoons whole-grain mustard, and 1/4 teaspoon salt, tossing to combine. Cook, covered, 5 minutes. Uncover and cook 8 minutes or until cabbage wilts, stirring occasionally. Stir in 1 tablespoon cider vinegar.
Combine 1/2 cup chopped mango, 1 tablespoon canola oil, 1 tablespoon fresh lime juice, and 1/4 teaspoon salt in a mini food processor; process until smooth.
Place 5 cups thinly sliced green cabbage, 1/2 cup diced mango, and 1/4 cup thinly sliced green onions in a large bowl, tossing to combine.
Drizzle cabbage mixture with pureed mango mixture; toss to coat.
Sprinkle with 3 tablespoons chopped toasted cashews.
Combine 4 teaspoons fresh lime juice, 4 teaspoons brown sugar, 2 teaspoons fish sauce, and 1 teaspoon sambal oelek in a small bowl.
Heat 1 tablespoon dark sesame oil in a large skillet over medium-high heat; swirl.
Add 8 cups sliced green cabbage to pan; cook 7 minutes or until lightly browned. Stir in brown sugar mixture; cook 4 minutes, stirring occasionally. Stir in 1/4 cup chopped fresh cilantro leaves.
