Preheat your oven to 350°F.
In a bowl, combine the strawberries with ¼ cup of the brown sugar and set aside to let macerate. Once juicy, mash ever so slightly with the back of a fork.
In a 2.25 quart braiser (or 10-inch baking dish), melt the butter over medium heat. Continue cooking, swirling occasionally, until the butter foams and turns golden brown with a nutty aroma, about 5–7 minutes. Immediately transfer the browned butter to a heatproof bowl to cool slightly. Keep your eyes on this - brown butter goes from perfection to too browned in a matter of seconds.
In a large mixing bowl, stir together the browned butter, remaining ¾ cup brown sugar, buttermilk, and salt until smooth.
Add the all-purpose flour, semolina flour, and baking powder. Stir until the batter is just smooth. Stir in the vanilla paste.
Generously grease a 10-inch braiser (or similar-sized baking dish) with non-stick spray.
Spoon the batter into the prepared dish, it will be thick, and spread it evenly. Spoon the mashed strawberries and their juices over the top.
Bake for 25–30 minutes, or until a toothpick inserted in the center comes out clean. Serve immediately with vanilla ice cream.