Mix together the 1 teaspoon salt, 1 teaspoon dried thyme, and ½ teaspoon ground black pepper.
Coat the 1 whole rabbit (2-3 pounds) with 2 Tablespoons vegetable oil. Sprinkle the seasonings over it, making sure to get all sides.
Smoke for about 2 hours, or until a meat thermometer reads 160℉ in the fattest part of the rear thigh. If desired, spritz with 4 Tablespoons apple cider vinegar every 30 minutes.
Let rest for 5 minutes before carving and serving.
Notes
Feel free to use your favorite BBQ rub or spice mix instead of the blend listed.If you want to use BBQ sauce, brush it on when the thigh registers 145℉ then continue to cook until it hits 160℉.