To dry brine the turkey, pat the turkey dry and season entire bird with kosher salt. Refrigerate overnight (or at least 8 hours).
Do not rinse.
Gently slip your hands under the skin to loosen it from the meat. Be careful not to puncture.
While your turkey is coming to room temperature, finely chop fresh spices.
Remove rosemary needles from stem and chop with kitchen shears.
Remove thyme leaves from the sprigs and chop with knife.
Remove oregano leaves from the stems and chop with a knife.
Remove sage leaves from stems and chop with a knife.
Whip softened butter until fluffy.
Add all finely chopped fresh spices to butter.
Add cajun seasoning, paprika, pepper and lemon juice to butter.
Whip with a hand mixer for about 5 minutes, scraping down sides of the bowl frequently.
Slide spoonfuls of butter under the skin on the breast.
Place the 2 whole onions, 2 lemon quarters, and half the carrots and celery in the cavity.
Insert a few sprigs of fresh herbs in as well.
Place remaining vegetables and lemons in bottom of roasting pan.
Place rack in roasting pan.
Coat turkey in a thick layer with about half of the butter.
Add broth to bottom of roasting pan.
Preheat oven to 400.
Heat remaining compound butter in microwave for 30 seconds, stirring and repeating until melted.
Fill meat injector with the liquid and inject just under the skin of each leg.
Cook for 45 minutes.
Fill injector and inject the breasts, legs, thighs and wings.
Remove from oven and reduce temperature to 325.
Cut cheesecloth to just cover top of turkey. Dip in melted compound butter to coat.
Tuck cheesecloth tightly around the top of the turkey.
Place back in 325 oven for 2-3 hours. Baste and check internal breast temperature every 45 minutes until it is at least 165.
Remove cheesecloth and allow to rest for at least 45 minutes.