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Beat together the cream cheese and the sugars on medium speed until smooth and creamy, scraping the sides of the bowl as needed, about 3 minutes.
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Add the pumpkin and mix on low until completely incorporated.
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Add the eggs one at a time, beating well until fully incorporated and scraping down the sides of the bowl between each addition.
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Add the heavy cream and vanilla and beat until well combined, about 1 minute. Add the cinnamon, ginger, salt, nutmeg, cloves and allspice and mix on low to incorporate.
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Pour the batter into the prepared crust. Tap the pan on the counter to release any air bubbles. Place the pan into a larger pan (a roasting pan is great for this) and pour the boiling water into the larger pan until it is about halfway up the springform pan.
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Bake for 55 to 65 minutes, or until the edges are set, but the middle still jiggles a little.
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Keeping the oven door closed, turn off the oven and let the cheesecake rest in the oven for 1 hour.
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After 1 hour, remove the cheesecake from the oven, carefully remove it from the water bath, remove the foil and place the cheesecake on a wire rack to cool completely, about an additional 2 hours. Once completely cool, refrigerate for at least 6 hours (preferably overnight).
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Cover any leftover cheesecake with plastic wrap and store in the refrigerator for up to 4 days. Wrapped, the cheesecake can be frozen for up to 2 months.