Trim any stems off the figs and cut them in half. Place them in a small saucepan and cover them them with the water. Cover the pot, place it on the stove, and bring it to a boil. Once it boils, reduce the heat to medium-low and simmer for five minutes.
While the figs heat, toast the mustard seeds in a dry skillet for 30 seconds to 1 minute, just until they start to pop. Transfer them to a plate to cool. Once they're cool, grind them in a spice mill or clean coffee grinder, and add them to the figs.
Add the sugar, lemon juice, vinegar, and salt to the fig and mustard slurry and stir to combine.
Using an immersion blender, puree the contents of the pot until mostly smooth. Cook, stirring constantly for a couple more minutes.
To can, funnel mustard into hot jars. Wipe the rims, apply lids and rings, and process in a boiling water bath canner for 15 minutes.
Notes
Recipe adapted from The New Persian Kitchen by Louisa Shafia.