In a medium saute pan, heat the oil until it begins to smoke lightly. Then add the onions and season with salt and pepper, to taste. 

Saute the onions until they give up their liquid, about 3 to 5 minutes, and then add the red wine. Lower the heat and cook the onions until the wine reduces almost completely. 

In a separate small pan, heat the honey on low to medium heat until it begins to bubble. Cook until the honey turns a light caramel color, an additional 2 to 3 minutes. 

Add the red wine vinegar, simmer for a few minutes on low heat, and then shut the heat off. Pour the honey mixture over the onions and continue cooking them over low heat for about 10 to 15 minutes. All of the juice should be absorbed and the onions should be a jam-like consistency.

Pour into a bowl and let rest.

Season and cool hamburgers as desired. We salt and pepper both sides and grill until they are medium done.

Once the burgers are done top with mayo, sliced brie and onion jam.