Preheat the oven to 250 degrees F. Line 2 baking sheets with silicone baking mats.
Combine the chickpea brine, sugar, lemon extract and cream of tartar in a stand mixer fitted with a whisk attachment and beat on high until stiff peaks form, about 10 minutes.
With a tablespoon-size ice cream scoop, drop scoops of the meringue batter onto the prepared baking sheets. With the back of the scoop, make a thumbprint on the top of each cookie with a swooping motion.
Bake for 45 minutes. Turn off the oven but do not open the door; leave the cookies in there for 2 hours to cool before removing.
Carefully lift each baking mat and gently peel it away from the cookies. Spoon a scant 1 teaspoon of the jam into the thumbprint of each cookie. Serve immediately; the cookies will soften within a few hours. Keep in an airtight container.