A barbecue cooking apparatus is provided. The barbecue cooking apparatus includes a firebox comprising a housing having solid walls. A charcoal tray is disposed within the housing, and one or more vents are disposed in the housing above the charcoal tray. One or more vents are disposed in the charcoal tray. An upper interior chamber within the housing above the charcoal tray is configured to hold wood and charcoal. A lower interior chamber within the housing below the charcoal tray is configured to provide a volume for the collection of wood ash. A duct is attached to the housing and forms a passageway from the lower interior chamber for heated air and wood smoke.