Step 1Heat the oven to 350 degrees. Butter a 9-inch square pan and lightly coat with flour. Tap out any excess flour.
Step 2Place the walnuts on a rimmed baking sheet and toast until lightly browned, 8 to 10 minutes. Let cool; coarsely chop.
Step 3Cream the butter and brown and granulated sugars until fluffy. Add the eggs; beat until smooth.
Step 4Add the applesauce, sour cream and rum or vanilla; mix well. Add the flour, walnuts, currants, cinnamon, baking soda, allspice, cloves and salt. Mix well. Transfer to the pan and smooth the top.
Step 5Bake until the cake is lightly browned and a toothpick inserted in the center comes out clean, about 50 minutes.
Step 1Combine the cream, butter and brown sugar in a small saucepan over medium-high heat, cooking until smooth, about 5 minutes. Remove from the heat. Stir in the rum or vanilla.
Step 2Heat the broiler with a rack 7 inches from the heat. Pour the glaze over the hot cake, gently brushing to evenly coat the top. Broil until the entire surface is bubbly, about 1 to 2 minutes.
Step 3Use a serrated knife to cut the cake into 12 or 16 pieces.