Preheat oven to 425°F (220°C). Cook rice in boiling water with salt for 15-18 minutes, then fluff and set aside.
Toss bell pepper, zucchini, red onion, and broccoli with olive oil, paprika, salt, and pepper. Roast for 20-25 minutes until tender.
Mix mayonnaise, vinegar, honey, salt, and pepper to make coleslaw dressing. Toss with cabbages and carrot. Chill until serving.
Season chicken breasts with salt and pepper. Sear in olive oil over medium-high heat for 4-5 minutes per side. Brush with BBQ sauce and cook 1-2 minutes more per side. Slice when cooked.
Divide rice among bowls, top with sliced BBQ chicken, roasted vegetables, and coleslaw. Drizzle with extra BBQ sauce if desired.
Notes
For extra flavor, brush the chicken with additional BBQ sauce before serving.