Dry brine your fresh turkey with kosher salt the night before by covering with salt and letting it sit in fridge overnight, covered. Use 1 Tbsp salt per 5 lbs of turkey. Do not rinse off the dry brine.
Make your Cajun butter by mixing all Cajun butter ingredients together in a medium bowl until well blended (it will look orange). Set aside half of the seasoned butter for Step 6.
Carefully separate the turkey skin from the meat and smother half of the remaining room temperature Cajun butter under the skin onto the meat. Use a spatula and move slowly so you don’t damage or rip the skin. Use the other half of the butter on the exterior of the turkey skin.
Place desired vegetables — such as carrots, onions, and celery — in the cavity of the turkey, and tie the legs with kitchen twine. Additionally, line the bottom of your large roasting pan with more vegetables of your choice and add chicken broth or white wine. Place the rack inside the roasting pan and lay the turkey on top.
Cook the turkey for 45 minutes at 400°F, then remove it from the oven and lower the temperature to 325 degrees.
Melt the remainder of the Cajun butter, and soak a cheesecloth inside. Cut the cheesecloth to fit your turkey, if necessary. Set aside.
Inject the turkey with melted Cajun butter. To do this properly, fill a clean meat injection syringe with the melted butter. Select about 8 spots, focusing on the thigh, breast, leg, and wing, and inject slowly until your butter is gone. Repeat as necessary until remaining butter is gone.
Lay the buttered cheesecloth over the turkey and cook for an additional hour. Keep the cheesecloth on and bask the turkey in the compound butter.
Cook turkey an additional 2-3 hours, checking the internal temperature every 45 minutes. Make sure the cheesecloth is snug against the turkey.
Remove the turkey from the oven when the thickest part of the meat reaches an internal temperature of 165°F at the center and the juices run clear. Allow the juicy turkey to rest on the stovetop for an hour before slicing.