Preheat oven to 350 degrees; spray sides only of 13x9 baking pan.
In a large mixing bowl combine flour, salt, baking soda, and both sugars
Cut butter into small pieces, and add to flour mixture.
Using a pastry blender or two forks, cut in butter until it is the size of peas.
Add the oats and vanilla and stir well.
Press the mixture into the bottom of your baking pan.
Bake for 20 minutes.
While the crust is baking, mix together the condensed milk, lemon zest, lemon juice, and egg yolks.
Remove crust from oven; pour lemon mixture over the crust.
Sprinkle blackberries over the lemon mixture; press down gently to cover.
Bake for an additional 20-22 minutes. (Lemon mixture should feel firm to the touch.)
Let cool completely, then refrigerate.
Optional: before serving, sprinkle each slice with powdered sugar.