Mix the kosher salt, brown sugar, and black pepper in a bowl.
Pat the turkey breast dry. Rub the mixture all over the turkey.
Place a raised rack in a deep roasting pan. Transfer the turkey breast to the rack. Refrigerate for at least 12 hours or up to 72 hours.
Roast the turkey:
Preheat the oven to 325ºF.
Remove the turkey from the refrigerator. See Note 1. Pour the olive oil on top and massage it over the breast with your hands.
Transfer to the oven and roast for 20 minutes per pound of turkey. For a 6-pound turkey, check the temperature after 1 hour 30 minutes and continue roasting until the turkey reaches 165ºF. Rotate the pan once midway through cooking to ensure even browning.
To serve:
Remove the turkey from the oven. Tent with foil and rest for 20 to 30 minutes. Slice the breast and serve immediately. Enjoy!
Notes
Note 1: I recommend lifting the entire rack out of the roasting pan and wiping out any liquid or spice mixture that has dripped onto the bottom of the pan before returning the rack back to the roasting pan.