Prepare a square 8x8 baking pan with parchment paper and set it aside.
Add the plums, sugar, brown sugar, and chai spice to a pot. Cook over medium-high heat for 10-12 minutes or until they release all their juices. Use a masher to mash them. Continue cooking for another 8 minutes, or until the jam is thick.
Whisk together the cornstarch and water and pour it into the pot.
Cook for another 5 minutes, or until the jam is even thicker and paste-like.
Transfer the jam into a small bowl and place it in the fridge to chill.
When the jam is completely cool, make the shortbread.
In a stand mixing bowl combine the butter, flour, sugar, brown sugar, and salt on low speed with the paddle attachment until the dough is crumbly and in pea sized pieces, this can take anywhere from 3-6 minutes.
Preheat the oven to 350 F/180 C.
Reserve ½ cup of the shortbread dough and set it aside.
Evenly press the rest of the shortbread into the prepared baking pan.
Evenly smear the cooled jam on top of the shortbread.
Sprinkle the reserved shortbread crumbs on top of the jam.
Bake for 33-38 minutes, or until the top of the shortbread is starting to turn golden brown.
Let the bars cool completely on a wire rack.
When cool, place the pan in the freezer for 15-20 minute to harden. Then remove them from the pan and use a sharp knife to cut them into clean bars. Dust with powdered sugar and enjoy!
Store leftover plum bars in an airtight container for 3-4 days at room temperature or in the fridge.