For the dry brine: The day before mix together the salt, pepper, oregano, sumac and onion powder in a small bowl. Place the turkey breast on a platter lined with 5 layers of paper towels. Using additional paper towels, pat the skin completely dry, then gently lift the skin and dry the meat. Flip the turkey breast over and season the underside with the dry brine; flip upright, lift skin and generously season the meat with the dry brine. Pat the skin down well and sprinkle any remaining dry brine over the turkey, then place in the refrigerator, uncovered, at least 8 and up to 24 hours.
The next day, remove the turkey breast from the refrigerator at least 1 hour before you're ready to cook it so it can come to room temperature on the counter. Preheat oven to 450 degrees F.
For the toum: Put the garlic, parsley, salt, sumac, and lemon zest and juice into the bowl of a miniature food processor and chop finely. Add the olive oil 2 tablespoons at a time, processing for 30 seconds between each addition, scraping down the bottom and sides of the bowl each time. Once all the oil is incorporated, drizzle in 1/4 cup water and process until smooth.
Place the turkey breast on a roasting rack, and once again pat dry both under and over the skin with paper towels. Rub a few tablespoons of toum in the cavity of the turkey breast; flip breast-side up, carefully lift the skin, and generously rub the toum all over the meat. Pat the skin to ensure the toum is well-distributed, then rub additional toum all over the skin.
Roast the turkey without opening the oven door, until an instant-read thermometer inserted into the thickest part of the breast reads 160 degrees F, 2 hours to 2 hours and 20 minutes. Allow to rest uncovered for 10 minutes before carving.