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1
Grease a 10-inch springform pan with 1 teaspoon of the butter.
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2
Combine the crumbs, 2 tablespoons of the sugar, and the melted butter in the bowl of a food processor and mix on low speed until well blended.
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3
Transfer to a greased 10-inch springform pan and press evenly around the bottom.
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4
Chill in the refrigerator for 1 hour.
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5
Preheat the oven to 325 degrees F.
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6
Combine the remaining 1/2 cup sugar and the water in a heavy, medium saucepan, and bring to a boil.
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7
Reduce the heat to medium and cook, stirring occasionally, until the sugar is dissolved.
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8
Continue cooking, swirling the pan occasionally, until the caramel is amber in color, 5 to 7 minutes.
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9
Add the remaining 4 tablespoons butter, stir, and cook over low heat until the butter is melted and evenly blended.
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10
Add the apples and stir to coat with the caramel.
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11
Cook, stirring, over medium heat until the apples are tender, about 5 minutes.
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12
Remove from the heat and let cool.
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13
Combine the cream cheese and brown sugar in a large bowl and beat with an electric mixer until smooth.
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14
Add the eggs 1 at a time, beating well after each addition and scraping the sides of the bowl as necessary.
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15
Add the lemon juice, cinnamon, and nutmeg and mix well.
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16
Fold the apple-caramel mixture into the batter, and pour into the chilled pan.
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17
Bake, rotating the pan a quarter turn every 30 minutes, until golden brown and firm around the edges, but still slightly loose in the center, 1 hour and 20 minutes to 1 hour and 30 minutes.
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18
Remove from the oven and cool for 2 hours.
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19
Cover the cheesecake and refrigerate for at least 4 hours, or overnight.
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20
To serve, spoon a portion of the Spiced Creme Anglaise onto each serving plate, top with a slice of the cheesecake, and drizzle with the Butterscotch Sauce.
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21
Prepare an ice bath by filling a large metal bowl with ice and water.
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22
Combine cream, zest, cinnamon, and nutmeg in a medium saucepan and bring to a simmer over medium heat.
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23
Remove from the heat.
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24
In a medium bowl, beat the egg yolks and sugar until pale and thick, about 2 minutes.
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25
Slowly drizzle in the hot cream, whisking constantly.
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26
Return the mixture to the pan and stirring constantly, cook over medium heat until the sauce thickens and coats the back of a spoon.
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27
Place in an ice bath and stir until cool.
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28
Cover with plastic wrap, pressing down against the surface to prevent a skin from forming.
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29
Refrigerate until well chilled, about 2 hours.
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30
Serve cold.
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31
Combine the sugar, water, and lemon juice in a medium, heavy saucepan and cook over medium-high heat, stirring, until the sugar dissolves.
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32
Let boil without stirring until the mixture becomes a deep amber color, 3 to 4 minutes, watching closely so it doesn't burn.
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33
Remove the pan from the heat.
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34
Add the butter and swirl the pan to melt it, about 1 minute.
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35
Return to the heat and bring to a boil.
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36
Add the cream, whisk to combine, and remove from the heat.
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37
Add 1/4 cup of the milk, then add up to 1/4 cup more until the desired consistency is reached.
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38
Cool until just warm before serving.
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39
(The sauce will thicken as it cools.)
