In a large bowl or zip-top bag, add your chicken breasts along with the olive oil and all of your seasonings. Toss to coat evenly.
Marinate for at least 30 minutes, or overnight in the fridge for best results. While the chicken marinates, add your purple cabbage, grated carrots, cashews, and green onions to a mixing bowl.
In a small separate bowl, whisk together the mayonnaise, honey, rice vinegar, soy sauce, chili garlic sauce, sesame oil, garlic, ginger, lime juice, and a pinch of salt until smooth. Pour the dressing over your slaw and toss to coat. Set aside in the fridge while you cook the chicken.
Take out a skillet or grill pan and set your burner to medium to medium-high heat. Once the pan is hot, cook the chicken for 5 to 8 minutes per side until nicely seared and the internal temperature reaches 165°F, about 10 to 16 minutes total depending on thickness. Remove the chicken from the pan and let it rest for a few minutes, then slice or chop into pieces.
Toast your bun if desired, then layer on your chili garlic slaw, sliced cucumbers, and chicken. Serve immediately and enjoy.