Whisk olive oil, soy sauce, garlic, brown sugar, and basil together in a bowl and pour into a resealable plastic bag. Add turkey breast, coat with the marinade, squeeze out excess air, and seal the bag. Marinate in the refrigerator, 8 hours to overnight.
Preheat the oven to 375 degrees F (190 degrees C). Line a roasting pan with aluminum foil.
Remove turkey breast from the marinade and shake off excess. Place turkey in the prepared roasting pan and season with salt and pepper. Set remaining marinade aside.
Cook turkey in the preheated oven for 1 hour. Baste with the reserved marinade and cook until no longer pink in the center and the juices run clear, about 20 minutes more. An instant-read thermometer inserted into the center should read at least 165 degrees F (77 degrees C).
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