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Preheat the oven to 350°F. Line the bottom of a 9-x-5-inch loaf pan with a rectangle of parchment paper. Spray the pan with non-stick spray, dust with flour, and tap out the excess.
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In a medium bowl, combine the flour, baking soda, salt, cinnamon, and nutmeg.
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In a large bowl (or in a stand mixer) beat the butter and brown sugar until light and fluffy, about 2 minutes. Beat in 1/4 cup of the caramel sauce and the egg. Add the flour mixture and beat on low speed just until combined. Beat in the applesauce just until combined.
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Spread the batter in the prepared pan and bake until cake springs back when pressed lightly, and a toothpick inserted in the center comes out clean, 40 to 45 minutes. Let the cake cool in the pan for 20 minutes, then turn out and cool completely on a wire rack. (Cake can be wrapped and frozen at this point for up to 3 months.)
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Before serving, drizzle the cake with the remaining 1/4 cup of caramel sauce and sprinkle with the pecans.