In a medium bowl, mash the ripe bananas with a fork until smooth but slightly chunky.
In a medium saucepan, combine the mashed bananas, granulated sugar, brown sugar, lemon juice, ground cinnamon, ground nutmeg, salt, and water. Stir well to combine.
Place the saucepan over medium heat and bring the mixture to a gentle boil, stirring frequently to prevent sticking.
In a small bowl, mix the cornstarch with 2 tablespoons of cold water until fully dissolved to create a slurry.
Once the banana mixture is boiling, slowly whisk in the cornstarch slurry.
Continue to cook the mixture, stirring constantly, until it thickens to a jam-like consistency, about 3 to 5 minutes.
Remove the saucepan from heat and stir in the vanilla extract.
Allow the jam to cool slightly before transferring it to a clean jar or airtight container.
Refrigerate the banana bread jam for at least 2 hours before serving to allow the flavors to meld and the jam to fully set.