Preheat oven to 350°F and line an 8-inch square baking pan with parchment paper.
Whisk together flour, baking soda, salt, and cinnamon in a medium bowl. Whisk together melted butter, sugar, brown sugar, vanilla, and lemon zest in a large bowl until combined. Add dry ingredients and fold in until incorporated.
Set aside ¾ cup (220 g) of dough for topping. Chill until ready to use. Press remaining dough evenly into bottom of prepared baking pan.
For 14 to 16 minutes, until lightly golden and set. Transfer to a wire rack and cool for 15 minutes.
Combine blackberries, sugar, salt, cornstarch, lemon zest, and lemon juice in a heavy saucepan over medium-high heat. Bring to a boil, pressing firmly on berries to release juices, about 3 to 4 minutes. Reduce heat to low and simmer for 1 to 2 minutes, until filling is thickened and coats the back of a spoon. Remove pan from the heat and cool filling for 10 minutes.
Spoon blackberry filling over cooled crust and crumble reserved dough over filling.
For another 40 minutes or until topping is golden and filling slightly bubbly. Cool completely in pan on a wire rack.
Just before cutting, chill in the freezer for 15 minutes. Carefully lift parchment and place bars on a cutting board; cut into squares with a sharp knife.
Store crumb bars in an airtight container in the refrigerator up to 3 days.
