In a Dutch oven or large, heavy pot, heat the oil over medium-high heat. Add half of the onions and cook, stirring, until dark golden brown and caramelized, about 15 minutes. Add the remaining onions and cook, stirring occasionally, until a deep caramel color, about 1 hour. Add the bourbon and cook, stirring occasionally, until evaporated, about 5 minutes. Add the remaining ingredients except the cheese, and stir well. Reduce the heat to medium-low and simmer, stirring occasionally, until thick and fragrant, about 1 hour. Remove from the heat and cover to keep warm.
To serve, sprinkle each portion with grated Swiss cheese.
Yield: 1 gallon