Heat the oven to 375°F. Line a loaf pan with parchment paper so there’s an overhang over the sides.
In a bowl, toss the blueberries with lime juice, sugar, and cornstarch. Set aside.
Brown the butter in a saucepan, swirling, until butter foams and starts to turn brown and smells nutty. Don’t let it get too brown, just golden with some brown flecks. Remove from the pan and let cool.
In a medium bowl, stir together the oats, flour, sugar, and salt. Pour in the browned butter and stir until clumps form. Use your hands to press together and make sure everything is slightly moist. The dough will be crumbly.
Take half of the crumble mixture and press evenly into the base of your pan. Spoon the berries evenly over the crust, leaving any juices behind and crumble the remaining dough on top.
Bake for 35-40 minutes or until the top is slightly brown and the fruit is bubbly. Let cool in the pan completely before cutting into squares.