Pat the turkey skin dry all over using paper towels.
Mix the sage, rosemary, thyme, lemon zest, and 2 tsp kosher salt in a small bowl, massaging it between your fingertips to help bring out the flavors.
Sprinkle the herb salt all over the turkey (underneath and on top) and rub it in. If you feel like you need more salt to get even coverage, sprinkle on another 1 tsp kosher salt and rub that in too.
Set the turkey on a wire rack over a sheet pan, sprinkle on any herb salt which has fallen off, and place in the fridge, uncovered, for 12-48 hours.
On the day of roasting, take the turkey out of the fridge and let sit at room temperature for 1 hour.
Preheat the oven to 400°F.
Place the carrots, celery, onions, rosemary sprigs, and thyme sprigs in a large roasting dish. Drizzle with 1 tbsp of the olive oil.
Set the turkey breast on top and drizzle with the remaining 2 tbsp olive oil.
Roast for around 1 hour 30 minutes, rotating the pan halfway through the cook time. The turkey is done once a thermometer inserted into the thickest part of the meat reads 165°F. Start checking after the 1 hour mark, and check every 10-15 minutes until the meat reaches the correct internal temperature.
Remove the turkey from the oven, transfer to a cutting board, and let it rest for 20-30 minutes.
Meanwhile, strain off the drippings from the roasting pan into a measuring jug. Top up with chicken or turkey broth to reach the 1 cup mark.
Mix the arrowroot starch with 1 tbsp water in a small bowl. Pour this into the jug of broth and whisk together.
Pour the stock mixture into a small pot and set over a medium-high heat. Whisk often until the mixture thickens then remove from the heat. Taste and season with tamari (or salt) and black pepper, as needed.
After the turkey has rested, remove the breasts from the bone, slice the breasts and then transfer to a platter and serve alongside the gravy.