In a large saucepan over medium heat, combine all of the ingredients. Bring to a simmer and then reduce the heat to medium low.
Cook until the fruit is soft enough to mash up, about 10 minutes. Let cool at least 15 minutes before using.
If you choose to use powdered Swerve as your only sweetener, don't add it along with the other ingredients. Whisk it in at the end, after the sauce comes off the heat, to avoid too much re-crystallization. Store the sauce in the fridge for up to a week. You can also freeze it for up to 3 months.