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1
At least 4 hours in advance, make the frosting: In a small saucepan, bring the apple juice concentrate to a boil; decrease the heat to medium-low and simmer for 20 to 25 minutes, or until the juice reduces to 3/4 cup (180 milliliters). It will thicken up, become syrupy, and boil a little slower as it reduces. Watch out that it does not over-boil or burn; you may need to decrease the heat as it thickens. To check to see if it is reduced enough, every now and then pour the juice into a measuring cup to measure it; if it is not 3/4 cup (180 milliliters), pour it back into the saucepan to continue to simmer and reduce until it measures the correct amount. Remove from the heat, transfer from the pan into a bowl, and cool in the refrigerator until cold to the touch.
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2
Using a stand mixer fitted with the whisk attachment (or an electric hand mixer), whip the cream cheese and 1/2 cup (120 milliliters) of the reduced apple juice concentrate on medium speed for 2 to 3 minutes, or until it is light and fluffy, scraping the bowl occasionally with a rubber spatula to get all of the cream cheese whipped up. (Reserve the rest of the apple juice for another use, such as adding it to oatmeal or drizzling on ice cream, or discard.) Slowly drizzle in the cream and beat on medium speed for 1 to 2 minutes, or until the cream thickens and combines with the cream cheese mixture. Add the cinnamon, vanilla, and salt and mix until well combined. Scrape the frosting into an airtight container and refrigerate for at least 4 hours or up to 3 days. The frosting needs to firm up before you can use it. You will have about 4 cups (960 milliliters) of frosting.
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3
Place a rack in the center of the oven and preheat to 350u00b0 F (175u00b0 C). Butter and flour two 8-inch (20-centimeter) round cake pans, or butter the pans and line the bottoms with parchment paper.
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4
Put the walnuts on a baking sheet and toast for 8 to 10 minutes, or until lightly toasted. Set aside to cool.
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5
Put the raisins and sultanas in a small bowl and pour hot water over to cover. Let sit for 30 minutes, then drain.
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6
In a medium saucepan, combine the apple juice concentrate and the juice from the pineapple chunks. Chop the pineapple into small pieces and set aside in a bowl. Bring the juices to a boil over medium-high heat, decrease the heat to medium-low, and simmer for 20 to 25 minutes, or until the liquid reduces to 3/4 cup (180 milliliters). (See step 1 under the frosting instructions for more details.) Remove from the heat, transfer to a bowl, and cool in the refrigerator until cold to the touch.
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7
In a large bowl, whisk together the apple juice concentrate, eggs, creme fraiche, milk, vegetable oil, vanilla, and reserved chopped pineapple until well combined. In a medium bowl, stir together the flour, baking powder, baking soda, salt, cinnamon, ginger, nutmeg, carrots, raisins, sultanas, and walnuts. Add to the egg mixture and fold together with a rubber spatula until well combined.
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8
Scrape the batter into the prepared pans, dividing equally. Bake for 35 to 45 minutes, or until the cakes are light brown (they won't color as much as a full-sugar cake) and spring back when you touch them in the center with your finger. They will not dome very much, if at all.
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9
Remove the cakes from the oven and let cool on a wire rack until you can pop them out of the pans. When the cakes are completely, totally cool (if they are at all warm, the frosting will melt off and it will be a mess), remove them from the pans. Using a long serrated knife, trim the tops of the cakes so they are level (they don't usually round too much, but it's nice to level them off if they do). Place one cake on a plate or cake pedestal (use a cake turner if you have one), and spoon about 1 cup (240 milliliters) of chilled frosting on top; using an offset spatula, spread the frosting evenly all the way to the edges of the cake.
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10
Carefully place the second cake on top of the first cake (place it upside down so the even, sharp edges will be on the top of your finished cake), and spoon about 1 cup (240 milliliters) frosting on top. Spread the frosting thinly to the edges and down the sides of the cake, smoothing it as well as you can and covering the entire cake with a thin layer of frosting. This layer of frosting is called a crumb coat; it keeps loose crumbs from migrating to the surface of the finished cake. (At this point, it helps to refrigerate the cake for about 15 minutes to help set the crumb coat; it's not crucial but if you have time, it makes frosting a little easier.)
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11
When you are done with the crumb coat, spoon a heaping 1 cup (240 milliliters) frosting on the cake and spread it evenly across the top and sides again. This is the final finishing layer of frosting. Fill a piping bag fitted with a small round tip with the remaining frosting, and pipe a border around the bottom of the cake, if you wish, or pile it on top of the cake.
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12
The cake can be stored in an airtight container in the refrigerator for up to 2 days. Any longer than that and the frosting will get softer and may slide off of the cake. Remove the cake from the refrigerator 2 to 3 hours before serving, garnish with fresh fruit or chopped nuts, and serve the cake at cool room temperature.
