In a large bowl, combine 1 cup of lukewarm water with salt, brown sugar, crushed garlic, peppercorns, allspice berries, thyme, and parsley. Stir until salt and sugar dissolve. Add 3 cups of cold water and mix well.
Place the turkey breast in a large resealable bag or container. Pour the brine over the turkey, ensuring it's fully submerged. Seal and refrigerate overnight or for at least 4 hours.
Remove the turkey from the brine, rinse under cold water, and pat dry with paper towels.
Preheat the oven to 375°F (190°C).
Line the bottom of a roasting pan with chopped carrot, celery, halved garlic head, and quartered onion.
Place the turkey breast on top of the vegetables. Drizzle olive oil over the turkey and sprinkle with ground black pepper. Tuck two sprigs of thyme under the turkey. Pour 1 cup of water or chicken stock into the pan. Cover the pan with aluminum foil and roast in the preheated oven for 2 hours.
Remove the foil and increase the oven temperature to 425°F (220°C). Continue roasting for an additional 30 to 45 minutes, or until the skin is golden brown and a meat thermometer inserted into the thickest part of the breast reads 165°F (74°C).
Remove the turkey from the oven and let it rest for at least 15 minutes before slicing. Serve with your choice of sides and enjoy!
