Cook rice as per directions on package; set aside once ready.
Steam the broccoli; set aside once ready. (See notes)
While the rice and broccoli cook, heat a large skillet over high heat. Once it's hot enough, which should take about 2 minutes, add 2 TBSP of the sesame oil. Swirl it around the pan to coat.
Add the ginger, garlic, scallions, and chiles, and stir immediately to prevent the garlic from burning. Fry for about 2-3 minutes, or until the garlic is fragrant and golden at the edges, stirring often. It's important to keep the garlic moving to prevent it from burning and becoming bitter.
Add the rest of the sesame oil to the pan as well as the cashews and the chicken. Sprinkle a bit of salt and pepper over the chicken, and cook for about 4-5 minutes, or until the chicken starts to brown, stirring occasionally. If the cashews seem to be browning to quickly, reduce the heat.
Lower the heat to medium and add the rice wine, soy sauce, and honey. Simmer until the sauce reduces into a thicker consistency and the chicken is cooked through. This should only take another 5-7 minutes.
Stir in the steamed broccoli and torn basil; garnish with sesame seeds and serve over rice.