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Put the pistachios and sugar to the bowl of a food processor and pulse to combine. Add water and blend until it resembles a chunky paste
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Move the pistachio paste to a small saucepan on medium heat, add milk and whisk over medium heat until hot
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Whisk together sugar, egg yolks, and cornstarch until combined - it will be thick
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Pour 1/4 cup of the hot milk mixture into the egg mixture and whisk, continue adding 1/4 cup of milk to eggs at a time 3 more times
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Return the milk with egg mixture to the saucepan on medium heat
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Heat until thick and bubbly, constantly whisking for about 1 minute or until thick
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Remove from heat, stir in butter, vanilla and almond extracts
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Push pudding through a fine mesh strainer into a bowl or container to make sure any cooked eggs are left behind, toss any nuts from the strainer into the bowl with the pudding
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Cover pudding with plastic wrap so that the plastic is on top of and touching the pudding (this will prevent the weird pudding skin from forming)
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Put the pudding into the freezer for about 15-20 minutes to get it to room temperature quickly
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While the pudding is chilling make the cheesecake and the crust
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Combine graham crumbs, chocolate, sugar, and melted butter
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Press into the bottom of and up the sides of a spring form pan
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Add all 5 blocks of cream cheese to the bowl of a stand mixer with the paddle attachment
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Whip the cream cheese on low for 2-3 minutes, until fluffy
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Sift flour and sugar together and add to cream cheese a little at a time until combined
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Add vanilla
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Crack eggs into a measuring cup and add to cream cheese one at a time, until combined -- CAREFUL not to over mix them or your cheese cake will have cracks, rise and sink
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Remove the bowl from mixer, tap on counter a few times so the air bubbles will rise, let sit for 20-30 minutes
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Melt chocolate chips and 1/4 cup of heavy cream in a small saucepan, stir to combine
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When melted and combined, add a couple of splashes of cream and combine, let cool to room temperature
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Divide cheesecake batter between 3 bowls evenly
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Fold in cherries and juice to the first bowl
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Fold in 1 cup of pistachio pudding to the second bowl
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Fold in melted chocolate to the third bowl
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Pour the cherry batter into the prepared crust and set on a flat surface in the freezer for 20 minutes, remove from freezer
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Using a soup ladle or large spoon and a spatula with wide holes, hold the spatula about 1 inch above the cherry batter and pour the pistachio batter over the spatula moving slowly around the pan until all pistachio batter is covering the cherry batter - this keeps them in layers
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Preheat oven to 350
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Put the pan back into the freezer for another 20 minutes
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Add the chocolate batter using the same process as with the pistachio
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Lay out 2 pieces of heavy duty foil in a deep roasting pan
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Carefully set the spring form pan on top of the foil and secure around the sides to keep the water bath separated
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Pour hot water into the roasting pan about halfway up the sides of the spring form pan
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Bake at 350 for 45 minutes
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Lower the heat to 325 for another 60 minutes or until set, checking after each 20 minute period
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Remove from heat, cool completely and refrigerate uncovered overnight