Preheat the oven to 425 degrees F. While oven is heating, pat turkey dry with a paper towel. Drizzle with 1 tablespoon olive oil all over. Season very generously on all sides with salt and pepper.
Place turkey breast on the rack of a roasting pan or on a baking sheet and roast for 15 minutes. Without opening oven, lower heat to 350 degrees F and continue roasting for about one hour, or until a cooking thermometer reads 155 degrees F when inserted into the thickest portion of the breast.
When cooked through, remove from oven, cover with foil, and let stand for 20 minutes. Once cool, use a sharp knife to slice in between the breastbone and turkey breast meat. Slice the meat away from the bone, then shred or dice.
In a large bowl, combine the broccoli slaw, scallion, cilantro leaves, 2 tablespoons olive oil, and lime and season generously with salt and pepper.
In a medium skillet over high heat, warm 1 tablespoon of olive oil until shimmering. Add the turkey, garlic, and chili powder and season with salt and pepper. Cook for 5 minutes, then remove from heat.
To serve, top turkey mixture with slaw, avocado, black beans, and radish.