Add blackberries, sugar, lemon juice, and vanilla extract to a heavy-bottomed saucepan. Place over medium heat. Place a small plate in the freezer.
Heat the blackberries until they begin to break down, and simmer into liquid. Bring the heat to medium-low.
Continue to cook, stirring almost constantly, until the blackberries are completely broken down, and the mixture is gelled, 20 to 30 minutes.
To test readiness, take the plate from the freezer, and spoon a small amount of the jam onto the plate. Jam should set up and be loose, but not runny. Run a spoon through the jam; if the line stays intact, the jam is gelled.
Remove the jam from the heat, and let cool completely. Stir in the lemon zest, and add the jam to jars to store.