In a medium heavy-bottom saucepan, combine the quartered figs, 1/3 cup packed brown sugar, grated lemon peel, 1/4 teaspoon kosher salt, and 1 teaspoon vanilla extract. Heat the mixture over medium heat until the figs release their juices and the mixture comes to a slow boil. Reduce the heat and simmer for 45 minutes, stirring occasionally and breaking up larger fig pieces with the back of a wooden spoon. Once thickened and softened, remove the pan from the heat and let the filling cool. For a smoother texture, you can puree the mixture using an immersion blender, blender, or food processor. I like to leave a few fig chunks for a more rustic filling.

Preheat the oven to 350°F (175°C). Line a 9x13-inch baking pan with aluminum foil, making sure the ends extend over the sides to help lift out the bars later. Spray the lined pan lightly with cooking spray. In a large microwave-safe bowl, melt 1 cup unsalted butter. Add the all-purpose flour, rolled oats, 1 cup brown sugar, 1/2 teaspoon salt, 3/4 teaspoon baking powder, and 2 teaspoons vanilla extract to the melted butter. Stir everything together until well combined and no dry streaks of flour remain. The mixture should be thick and crumbly; you may find it easier to finish mixing with your hands. For extra depth, I like to briefly toast the oats in a dry pan before adding them to the crust mixture.

Reserve 1 1/2 cups of the oat crust mixture for the topping. Press the remaining mixture evenly into the bottom of the prepared pan, using the bottom of a glass or your hands to flatten it into a solid, even layer. Spoon the cooled fig filling (from Step 1) over the crust and spread it out to cover the surface evenly. Crumble the reserved 1 1/2 cups of oat mixture evenly over the fig layer, allowing some bits to peek through for a pretty, rustic look.

Bake the assembled bars in the oven at 350°F (175°C) for 30-35 minutes, or until the jam is bubbling and the crumb topping is golden brown. Allow the bars to cool completely in the pan. Once cooled, lift the bars out of the pan using the overhanging foil. Slice into bars and serve. For neater slices, I like to chill the bars in the fridge for 30 minutes before cutting.