Preheat the oven to 350 degrees. In a large bowl, toss the strawberries with the sugar, lemon juice, cornstarch slurry, and vanilla seeds and let stand until the berries release some of their juices, about 30 minutes. Pour the fruit filling into a 9-by-13-inch glass or ceramic baking dish set on a sturdy baking sheet.

In a medium bowl, mix all of the ingredients with your fingers until a coarse meal forms; press into small clumps.

In a medium bowl, whisk the flour with the baking powder and salt. In a large bowl, using a handheld electric mixer, beat the butter with the sugar at medium-high speed until light and fluffy, about 3 minutes. Add the eggs, one at a time, beating well between additions. Beat in the vanilla extract and scrape down the bowl. Add the dry ingredients to the batter in 3 additions, alternating with the buttermilk.

Spoon the batter over the fruit filling, spreading it to the edge. Sprinkle with the crumb topping. Bake in the center of the oven for 1 hour and 15 minutes, until the fruit is bubbling, the crumb topping is golden and a toothpick inserted in the center of the cake comes out with a few moist crumbs attached. Transfer to a rack to cool slightly. Serve the crumb cake warm or at room temperature.

The crumb cake can be refrigerated overnight. Serve warm or at room temperature.