In a large bowl, toss the strawberries with the balsamic, sugar, cornstarch, salt, and pepper. Let sit while you make the topping, stirring once or twice — the sugar and cornstarch will start pulling juice from the berries and thickening it into a light syrup.
2 ¼ pounds strawberries, 3 tablespoons good aged balsamic vinegar, 6 tablespoons granulated sugar, 1 ½ tablespoons cornstarch, Pinch kosher salt, Scant ¼ teaspoon freshly cracked black pepper
Melt the butter in a small saucepan over medium heat, swirling occasionally, until it foams, turns golden, and smells nutty, about 5 minutes. Pour into a bowl, stir in the vanilla extract, and set aside to cool slightly.
12 tablespoons 1½ sticks unsalted butter
In a medium bowl, combine the oats, flour, almonds, brown sugar, granulated sugar, and salt. Pour the cooled brown butter over the dry mixture and toss with a fork until it forms small, even clumps.
1 teaspoon pure vanilla extract, 1⅛ cups old-fashioned rolled oats, ¾ cup all-purpose flour, ½ cup sliced almonds, ½ cup light brown sugar, 3 tablespoons granulated sugar, ½ teaspoon kosher salt
Preheat the oven to 375 degrees Fahrenheit (190°C). Pour the strawberry mixture into a 2-quart baking dish or deep 9-inch pie dish. Top evenly with the crumble, breaking up any large clumps as you go.
Bake until the topping is deep golden and the juices are bubbling at the edges, 32 to 38 minutes.
Let the crumble rest for 5 minutes before serving — the filling needs a minute to set, and it gives the ice cream a fighting chance not to vanish on contact.
Spoon into bowls, top with a generous scoop of vanilla bean ice cream, a scatter of basil, a few strokes of lemon zest, and a pinch of flaky salt. Serve immediately.