Add frozen fruit and any optional ingredients to a medium saucepan. You can use fresh fruit, but you may want to add some water as you cook to get the right consistency.
Dissolve cornstarch in water; start with just 1 tbsp cornstarch. Add to fruit and bring to a boil.
Lower to simmer and reduce for about 10-15 minutes, until it reaches your desired consistency. Add extra cornstarch dissolved in a bit of water to thicken as needed. Note that the jam will thicken as it cools, too.
Use an immersion blender, transfer to a regular blender, or just keep it chunky. Whatever you like!