In a medium saucepan, combine mashed bananas, granulated sugar, brown sugar, lemon juice, ground cinnamon, ground nutmeg, salt, and water.
Place the saucepan over medium heat and stir the mixture continuously until the sugars dissolve and the mixture begins to simmer.
Reduce the heat to low and let the mixture simmer gently, stirring frequently, until it thickens to a jam-like consistency, about 30 to 35 minutes.
Remove the saucepan from heat and stir in the butter and vanilla extract until fully incorporated.
Allow the jam to cool slightly before transferring it to sterilized jars.
Let the jam cool completely at room temperature, then seal the jars and refrigerate.
Store the banana bread jam in the refrigerator and consume within 2 weeks.