Combine quartered figs, brown sugar, lemon zest, kosher salt, and vanilla extract in a medium heavy-bottom saucepan. Cook over medium heat until figs release juices and mixture comes to a gentle boil.
Reduce heat and simmer for 45 minutes, stirring occasionally and mashing pieces.
Remove from heat and cool. Puree filling to smooth consistency if desired.
Preheat oven to 350°F. Line a 9x13-inch pan with foil and spray with nonstick cooking spray.
In a large bowl, melt butter. Add flour, oats, brown sugar, salt, baking powder, and vanilla extract. Stir until well blended.
Reserve 1 1/2 cups of oat mixture. Press remaining mixture firmly into prepared pan to form base.
Spread cooled fig filling over base. Crumble reserved oat mixture evenly over filling.
Bake for 30 to 35 minutes until filling bubbles and topping is golden.
Cool completely in pan. Use foil to lift slab and slice into bars.
For neat slices, chill before cutting with a sharp knife.