Apples:
2 tablespoons unsalted butter
3 Honeycrisp or Cortland apples (1 1/2 pounds), peeled and cut into 1/3-inch pieces
1/2 cup raisins
1/2 cup sugar
1 teaspoon fresh lemon juice

Streusel:
3/4 cup all-purpose flour
1/4 cup plus 2 tablespoons light brown sugar
1 tablespoon finely chopped pecans
6 tablespoons cold unsalted butter, cut into cubes

Cake:
4 tablespoons unsalted butter, plus more for greasing
1 1/2 cups all-purpose flour, plus more for dusting
1 1/2 teaspoons baking powder
1/2 teaspoon baking soda
1/4 teaspoon ground allspice
Pinch of kosher salt
3/4 cup sugar
1 large egg, beaten
2/3 cup buttermilk
Whipped cream, for serving

Prepare the Apples
In a large skillet, melt the butter. Add the apples, raisins, sugar and lemon juice and cook over moderately high heat, stirring often, until the sugar is dissolved, about 5 minutes. Continue to cook the apples over moderate heat, stirring occasionally, until they’re very soft and caramelized, 20 to 30 minutes; add water by the tablespoonful if the apples get too dry. Let cool to room temperature.

Meanwhile, Make the Streusel
In a medium bowl, combine the flour, sugar and pecans. Rub the butter into the mixture until coarse crumbs form.

Make the Cake
Preheat the oven to 350°F. Butter and flour a 9-inch square baking pan. In a medium bowl, combine the 1 1/2 cups of flour with the baking powder, baking soda, allspice and salt. In another medium bowl, using a handheld electric mixer, cream the 4 tablespoons of butter with the sugar until fluffy and pale yellow, about 3 minutes. Beat in the egg until incorporated. At low speed, beat in the buttermilk and the flour mixture in 3 alternating batches, ending with the flour mixture. Fold in the apples.
Scrape the batter into the prepared pan and smooth the surface. Sprinkle the streusel evenly over the batter and bake for about 45 minutes, until a cake tester inserted in the center comes out clean. Transfer the cake to a rack and cool completely. Serve with whipped cream.

MAKE AHEAD The cake can be stored overnight in an airtight container at room temperature.