Brown the butter. Melt the butter in a light-colored saucepan over medium heat. Continue cooking and stirring until it foams and develops golden-brown flecks with a nutty aroma. Immediately pour it into a heatproof bowl, including all the toasted brown bits. Let cool for about 10 minutes.
Prepare the pan. Heat the oven to 350°F. Line an 8-inch square baking pan with parchment paper, leaving enough overhang to lift the bars out later.
Make the crumble mixture. In a large bowl, combine the flour, oats, brown sugar, cinnamon, and salt. Stir in the browned butter and vanilla until moist crumbs form.
Make the crust. Reserve about 1½ cups of the crumble mixture for the topping. Firmly press the remaining mixture into the bottom of the prepared pan. Bake for 10 minutes.
Prepare the blueberry filling. Gently toss the blueberries with the sorghum syrup, lemon juice, lemon zest, cornstarch, and a pinch of salt until evenly coated.
Assemble. Spread the blueberry mixture evenly over the warm crust. Sprinkle the reserved crumble generously over the berries, leaving a few blueberries peeking through.
Bake. Bake for 35–45 minutes, until the blueberry filling is bubbling around the edges and the crumble is deeply golden.
Cool completely. This part matters! Let the bars cool completely in the pan before slicing so the blueberry filling has time to set.