Combine everything over medium heat and bring to a simmer. Let cook for a minute or two, then taste and adjust seasonings. If your jam is very sweet, for example, you might want to add more vinegar and/or mustard.
Depending on the jam, your BBQ sauce might be quite chunky. For a smoother sauce, blend with an immersion blender.
Serve hot with tofu, tempeh, or whatever else your heart desires.
This is a great way to use up leftover jam, but since they come in so many different varieties and levels of sweetness, you might have to do a lot of tasting and seasoning to get your sauce just right.