In a large saucepan, over medium heat, heat the oil. Add the yellow onion, red onion, and shallots to the pan and stir well. Season the onions with salt, and pepper, to taste.
When the onions have cooked down and they are deepening in color, deglaze the pan with the red wine. Let the wine cook until reduced and absorbed by the onions. Cook the onions for about 5 minutes more, then add the cherry juice and red wine vinegar. Reduce the heat to medium-low heat, and let cook at a slow simmer. Add the thyme, rosemary, and bay leaf. Let the onions cook down until they start taking on a soft texture and the liquid is reduced and absorbed by the onions. Stir in 2 tablespoons brown sugar and honey. Cook, stirring occasionally until the liquid has reduced and the onions have absorbed most of the liquid, about 8 to 10 minutes. Taste the mixture and add more sugar if it is too tart. Test the consistency of the jam by drizzling a spoonful of it onto a plate and letting it cool. It should be thick and not runny. If it is too runny, simmer the mixture longer until more liquid is cooked out.
Serve the jam with pork, beef, chicken, or fish, or try it with roasted vegetables.
The salt will help the onions cook down because they will pull moisture.
This recipe was created by a contestant during a cooking competition. It has not been tested for home use.