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For the Crust: Position rack in center of oven. Preheat oven to 375°F/190°C. Coat the inside of a 9-inch (23 cm) springform pan with nonstick spray. Double wrap the outside of the pan with extra-wide aluminum foil, bringing the foil all the way up and around the sides of the pan to the top edge; set aside.
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Grind the cookies to a fine crumb in a food processor fitted with a metal blade. Alternatively, place in heavy zip top bag and crush well with a rolling pin. Use a rolling and a smashing action to get the job done. Stir in melted butter to evenly moisten crumbs. Press crust mixture firmly into an even layer covering the bottom of the prepared pan.
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Bake for about 10 to 12 minutes or until light golden brown. You want the cookies to dry out a bit. Remove crust from oven and set aside on rack. Turn oven down 325°F/165°F.
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For the Cheesecake: Meanwhile, prepare the cheesecake batter. Lactose-free cream cheese acts differently from regular cream cheese so please follow our technique: place one container of cream cheese in a mixing bowl and blend on low speed with an electric mixer until creamy and smooth. Add sugar, pumpkin purée, spices and vanilla and blend very briefly on low speed. Pour in eggs a little bit at a time, mixing just enough to incorporate and no more. Mixture might be very liquid at this point; that’s okay. Add remaining cream cheese and beat just until combined, about 30 seconds to 1 minute. If the cream cheese is resisting being combined with the initial mixture, use a large balloon whisk and combine by hand using a folding action. Make sure mixture is well combined but do not over mix. Gently whisk in sour cream by hand. Scrape cheesecake batter over crust.
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Place aluminum foil wrapped pan in a large roasting pan. Add very hot tap water to roasting pan to come up sides of springform pan about 1-inch (2.5 cm). Bake for 1 hour to 1 hour and 5 minutes. Cake should be set along the edges and slightly giggly in the center. Turn oven off, leaving cake in oven for 15 minutes more. Remove from oven. Dip the tip of a small paring knife in warm water and use it to run around the top edge of the cake (going down about 1/2 inch/12 mm) to loosen it from the pan; this will prevent the sides from pulling away from the pan, which can create cracks. Remove cake pan and remove foil. Refrigerate overnight or up to 48 hours. Dip a small icing spatula in warm water, shake dry, and run all the way around the outer edge of the cake going all the way down to the bottom to loosen cake from pan. Release springform, remove and place cake on a display plate.
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Cake is ready to serve or may be refrigerated until serving time, preferably within the day. Cheesecake is best served cold. Use a long, thin bladed knife dipped in hot water to make cuts and wipe clean between cuts. The cake can be refrigerated for up to 3 days, although the crust will lose its crispness.