To prepare turkey brine, bring 2 cups of water to a boil in medium pot. Add the salt and sugar and stir to dissolve. Remove the pot from heat, add the rest of the ingredients, stir and let cool to room temperature. If pressed for time, let the vegetables and the spices steep for 10 minutes, then cool down with ice. Remember to account for the extra ice.Combine with the rest of the water and set aside.
Put the turkey breast in the brine, and refrigerate for two hours for a small breast, 3 hours for a medium and 4 hours for a large turkey breast. Make sure that the breast is fully covered in brine. You can use a bowl or a Ziploc bag.
Preheat oven to 400F.
Dry the breast with a paper towel and rub with olive oil. Season with salt and spices on all sides and gently pat to make the seasonings stick.
Heat 1/2 cup of cooking oil (you can use olive oil or any other oil you prefer) in a large skillet over medium-high heat. Place the turkey breast skin side down on the skillet and cook for 2 minutes. Flip and continue cooking for another 2 minutes. Remove from the skillet and set aside.
Carefully pour out or wipe off with paper towels all the oil from the pan. Put the breast back in the skillet, bone side down.
Now put the skillet with the turkey breast in the oven and roast at 400F for about 45 - 75 minutes, depending on the size of the breast, or until internal temperature of the meat reaches 160F.Let rest for 5 minutes and serve.