Line an 8x8 baking dish with parchment paper.
Make the plum jam. In a small pot, add plums, granulated sugar, brown sugar and cook over medium heat, stirring occasionally for about 10 minutes. Plums will start to break down. Place the plum mixture into a blender and blend until smooth. Place back in pot and continue cooking for another 8 minutes.
Mix water with cornstarch and then add to plum mixture. Continue to cook on medium heat until sauce has thickened. Plum jam should be a paste like consistency. Transfer to a bowl and let cool.
In a medium sized bowl, mix flour, salt, brown sugar, and granulated sugar. Add in cold butter and vanilla extract. Using a handheld mixer, or stand mixture, mix on low speed until crumbly and pea sized bits.
Preheat oven to 350 degrees.
Press flour mixture evenly into bottom of 8x8 baking dish, reserving 1/2 cup.
Top with an even layer of cooled plum jam.
Sprinkle remaining flour mixture on top.
Bake 35-40 minutes.
Once cooled, slice into bars and enjoy!