Start by placing your autumn olive berries in a large pot with water. Use 1 cup of water per pound of fruit, so for this recipe, you'll need 3 cups of water for the 3 lbs (10-11 cups) of berries. Bring the mixture to a boil, then simmer the berries for 1 to 2 minutes, just until they start to fall apart.
Once the berries are softened, strain the mixture through a food mill or fine-mesh strainer. You should end up with about 6 cups of smooth autumn olive pulp.
Transfer the strained pulp back into your pot. Bring it to a boil, then add the powdered pectin (skip the sugar for now). Boil the pulp and pectin together for about 1 minute, stirring constantly to ensure the pectin dissolves and incorporates.
After the pectin is fully mixed in, add your desired amount of sugar. For a low-sugar version, use between 1 to 2 cups of sugar. For a sweeter jam, go up to 4 cups. Stir in the sugar along with the cinnamon and ground ginger, and bring the mixture back to a boil for 1 minute, stirring often.
Remove the pot from heat and ladle the jam into prepared sterilized jars, leaving 1/4 inch of headspace. If you’re canning, process the jars in a boiling water bath for 10 minutes (or 15 minutes if you’re above 6,000 feet in elevation). Allow the jars to cool completely on a towel, and check the seals before storing. Unsealed jars should be kept in the refrigerator and used right away.