Cook chicken. Rub breasts with oil, chili powder, garlic powder, salt, and pepper. Grill or pan-sear over medium heat until cooked through (internal temp 165°F / 74°C), 5–7 minutes per side. Rest 5 minutes, then cube.
Make dressing. Whisk olive oil, lime juice, zest, honey, Dijon, garlic, salt, and pepper until glossy.
Build salad. In a large bowl, add cabbage, mango, cucumber, red onion, jalapeño, and cilantro. Toss with half the dressing.
Finish. Fold in chicken and avocado. Drizzle the remaining dressing. Top with nuts. Taste and adjust lime, salt, or honey.
Serve. Enjoy right away or chill 15 minutes for extra flavor.