Put a few spoons in the freezer. Then add the figs, sugar, lemon juice, and lemon zest to a medium saucepan and bring to a boil over medium high heat.
Cook for about 20 minutes. Stir often using a wooden spoon to ensure that the larger fruit chunks get broken up and to avoid sticking. As the jam begins to thicken, you may want to lower the heat a bit.
At around the 20 minute mark (or when your jam seems sufficiently thick and, well, jammy), test for donenness. To do this, put a drop on one of your freezer spoons and run a finger through it. If it creates a track instead of running back into the space that your finger touched, it's done! If it's not quite ready, try again in a few minutes with one of your other freezer spoons.
Stir in vanilla extract and transfer to a jar. Store in the fridge for up to 3 weeks, or freezer for a few months!