Rinse the turkey and pat it dry. Combine the paprika, onion powder, garlic powder, chili powder, black pepper, basil, oregano, salt, cayenne pepper, and cumin in a small bowl. Rub the spice mixture all over the turkey and in its cavity. Put the turkey in a roasting pan, cover it with foil or plastic wrap, and refrigerate it for at least 2 hours.
Assemble the burner, propane tank, and large pot of your frying kit on a solid, level, non-flammable surface (like brick or concrete). Fill the pot about halfway (but no more than halfway) with the peanut oil, and heat it to 350°F. Do not overfill the pot with oil!
Put the turkey in a turkey basket or on a turkey stand and slowly and carefully lower it into the hot oil with a hook. (Do not drop it quickly!) Do not leave the turkey unattended after lowering it into the oil, and periodically check the temperature of the oil and adjust the heat as necessary to keep it at 350°F. Cook the turkey until its internal temperature reaches 170°F in the breast and 180°F in the thigh, 40 to 45 minutes.
Turn off the heat. Carefully remove the turkey from the oil with the hook, and transfer it to a roasting pan or a disposable foil tray. Let it sit at room temperature for at least 10 minutes before carving and serving. (Store leftover turkey wrapped in foil in the refrigerator for up to several days.)
