The batter for this cake is much like that for a biscuit; the chilled butter is cut in rather than creamed to produce a tender crumb. This recipe was developed by Emily Donahue for Roseys Coffee and Tea in Hanover, New Hampshire.
Preheat oven to 350 degrees. Brush a 9-by-12-by-3-inch baking pan with butter, and set aside. Make fruit sauce: Combine lemon juice, cornstarch, and 1 cup sugar in a medium saucepan. Add strawberries and rhubarb; cook, stirring frequently, over medium heat, until rhubarb is soft and liquid has thickened, 15 to 20 minutes. Transfer to a medium bowl; let cool.
Make the crumb topping: Combine 3/4 cup sugar and 3/4 cup flour in a medium bowl. Melt 1/4 cup butter in a small saucepan over low heat. Drizzle butter over flour mixture; using your hands, mix until crumbly. Set aside.
Make cake batter: Whisk together remaining 3 cups flour and 1 cup sugar, baking powder, baking soda, and salt in a large bowl. Using a pastry knife or two forks, cut butter into flour mixture until it resembles coarse meal. In a separate bowl, mix eggs, buttermilk, and vanilla. Pour into flour mixture; stir to combine.
Spread half the cake batter evenly into the prepared pan. Top with half the fruit sauce. Carefully spread the remaining batter over the fruit, and top with the remaining fruit sauce. Sprinkle with the crumb topping.
Bake until cake is golden brown and springs back when touched in the center, about 1 hour. Transfer pan to a wire rack to cool slightly. Serve warm or at room temperature, cut into squares.