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Preheat oven to 350°F. Grease a 9x5-inch loaf pan and line the bottom with parchment. Dust the sides with flour and tap out the excess.
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In a small bowl, stir the ground flax seeds with 3 tablespoons of water. Set aside for 15 minutes to thicken.
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In a large bowl, beat the shortening and sugar with an electric mixer until light and fluffy, about 3 minutes. Beat in the maple syrup and flax-water mixture. Sift the flour, baking soda, salt, cinnamon, nutmeg, and ginger into the bowl and beat to combine. Beat in the applesauce.
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Spread the batter into the prepared pan and bake until a toothpick inserted in the center comes out clean, 45 to 55 minutes. Cool the cake in the pan on a wire rack, then run a knife around the edges and turn the cake out. Store loosely wrapped at room temperature.