Combine the quartered figs, 1/3 cup packed brown sugar, grated lemon peel, 1/4 teaspoon kosher salt, and 1 teaspoon vanilla extract in a medium heavy-bottomed saucepan. Heat 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 large fig pieces with the back of a wooden spoon. Once thickened, remove from heat and allow the mixture to cool. If you prefer a smoother texture for the filling, blend it using an immersion blender, blender, or food processor.

Preheat your oven to 350 °F (175 °C). Line a 9x13-inch baking pan with aluminum foil, leaving some foil hanging over the sides for easy removal later. Lightly spray the foil with cooking spray. In a large microwave-safe bowl, melt the unsalted butter. Add the flour, rolled oats, brown sugar, salt, baking powder, and vanilla extract to the melted butter. Mix until well combined with no streaks of flour remaining; the mixture will be thick and may require mixing by hand. I like to use my hands to ensure everything is evenly incorporated for a crumbly, rustic texture.

Set aside 1 1/2 cups of the oat mixture from Step 2 to use as the crumble topping. Press the remaining oat mixture firmly into the bottom of the prepared pan, using the bottom of a glass or your hands to form an even layer. Spread the cooled fig filling (from Step 1) evenly over the crust. Crumble the reserved oat mixture over the top of the fig filling for a rustic finish.

Bake the assembled fig bars in the preheated oven for 30-35 minutes, until the top crumble is golden brown and the jam is bubbling around the edges. Remove from the oven and let the bars cool completely in the pan. Once cooled, lift the bars out using the overhanging foil, slice into squares or bars, and serve. For a neater presentation, I like to chill the bars briefly before slicing—they hold their shape better that way!