1. Prepare marinade: In a small bowl, whisk together lime juice, 6 tbsp olive oil, tamari, cilantro, mint, shallot, red pepper, maple syrup, and black pepper.
2. Pound chicken between 2 sheets of plastic wrap to an even thickness. Place chicken in a glass container and pour ½ cup marinade over chicken. Cover and refrigerate for at least 1 hour and up to 12 hours.
3. Prepare dressing: Add remaining 3 tbsp olive oil and ¼ tsp salt to remaining marinade. Set aside.
4. Cut off broccoli stems and trim tough outer peel. Chop into 2-inch pieces and place in a food processor. Cut the tops into large florets and add to bowl of processor. Pulse a few times until broccoli resembles rice. (If your food processor is small, do this in batches.)
5. Heat an indoor grill or grill pan to medium-high. Remove chicken from marinade and discard excess. Grill until cooked through, about 6 minutes each side. Transfer to a cutting board and cover with foil to keep warm.
6. In a large skillet on medium, heat coconut oil. Add garlic and sauté for 20 seconds, or until fragrant. Add riced broccoli and remaining ¼ tsp salt, and sauté for 5 minutes, or until desired tenderness is achieved.
7. Divide riced broccoli among bowls. Dice chicken and add to bowls. Add carrots, cabbage, avocado, kohlrabi, and radish. Drizzle with reserved dressing and garnish with cashews and additional cilantro and mint.