Place the Amaretti cookies in a food processor and pulse until finely ground.
Transfer the crumbs to a bowl, add the melted butter, and mix until combined.
Spread the crust into the prepared pan and evenly press them into the bottom and halfway up the sides. Bake for 8 minutes; set aside.
When the pan has completely cooled, place it on the middle of two large pieces of aluminum foil (laid out in a cross shape) and fold up the sides around it, until it reaches the top. Tightly shape the foil around the pan.
To prepare the filling, preheat the oven to 325°F.
Blend the ricotta in a food processor until smooth. Spoon the cheese into the bowl of a stand mixer fitted with a paddle attachment. Add the mascarpone cheese and mix until combined. Add the sugar, lemon juice, and vanilla. Mix until combined, then pause to scrape down the sides of the bowl. Add in and the eggs and mix just until blended.
Pour the mixture onto the crust. Place the cheesecake into a large roasting pan. Fill the roasting pan with enough hot water to cover the cheesecake pan halfway. (The foil will prevent the water from leaking into the cake.) Bake until the center of the cake moves slightly when the pan is gently shaken, about 90 minutes. Transfer the cake to a rack and cool for 45 minutes. Refrigerate until cold, at least 8 hours or overnight.
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