Instructions

1. Make cake:
2. Place 4 tablespoons unsalted butter in the bowl of a stand mixer (or large bowl if using an electric hand mixer). Let sit at room temperature until softened. Arrange a rack in the middle of the oven and heat the oven to 350°F. Coat an 8x8-inch square pan with butter, then coat with flour and tap out the excess.
3. Add1 cup granulated sugar and 1 large egg to the butter. Beat on medium speed until light and fluffy, 2 to 3 minutes. Add 1 cup unsweetened applesauce and beat until combined.
4. Place 1 1/2 cups of the all-purpose flour, 1 teaspoon baking soda, 1 teaspoon ground cinnamon, 1/2 teaspoon ground cloves, and 1/4 teaspoon ground allspice in a medium bowl and whisk to combine. Add to the applesauce mixture and beat on low speed until combined.
5. Place the remaining 1 tablespoon all-purpose flour, 1 cup chopped walnuts, and 1 cup raisins in the now-empty bowl and toss to combine. Add to the cake batter and fold in by hand with a rubber spatula until combined. Pour the batter into the baking pan.
6. Bake until a toothpick inserted in the center comes out clean, 35 to 40 minutes. Let cool completely on a wire rack, then cut into squares to serve.
7. Make hot rum sauce:
8. Whisk 1 large egg in a small bowl until broken up.
9. Place 1/3 cup granulated sugar, 2 tablespoons cornstarch, and 1/4 teaspoon kosher salt in a small saucepan and whisk to combine. Add 2 cups whole milk, whisk to combine, and bring to a boil over medium heat. Reduce the heat to low and cook, stirring constantly, until the mixture is thickened, 3 to 5 minutes.
10. Add a small amount of the warm sauce to the egg and whisk thoroughly to temper the egg. Pour the mixture into the saucepan and whisk until smooth. Cook, stirring constantly, until the mixture is thickened, 3 to 5 minutes. Remove from the heat. Add 1/4 cup light rum and 1 teaspoon vanilla extract and stir until well-blended. If desired, the sauce can be strained through a fine-mesh strainer before serving.
11. To serve, pour the rum sauce over each cake square. Serve with more warm sauce if desired.