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1
Position oven rack in the middle of the oven; preheat oven to 350u00b0.
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2
Generously butter the bottom and sides of a 9-inch springform pan.
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3
Make the crust: pulse the pecans, flour, and sugar in a food processor until the nuts are finely ground.
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4
Add the butter and pulse just until combined; press the crust evenly over the bottom and 1 inch up the sides of the pan.
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5
Bake for 10-12 minutes, until light brown.
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6
Transfer to a wire rack and cool completely; decrease oven temperature to 300u00b0.
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7
Make the filling: mash the blackberries and sugar together in a medium saucepan with a pastry blender or fork.
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8
Cook over medium heat, stirring occasionally, until the berries begin to release their juices.
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9
Stir in the cornstarch, bring to a boil over med-high heat, stirring constantly, and boil for 1 minute.
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10
Pour the puree through a coarse strainer set of a small bowl, pressing hard on the solids to extract as much liquid as possible.
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11
Refrigerate, tightly covered, until thoroughly chilled.
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12
Using an electric mixer on med-high speed, beat the cream cheese in a bowl for about 2 minutes, until light and fluffy.
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13
Gradually beat in the condensed milk, zest, lime juice, and vanilla, scraping down the side of the bowl as necessary.
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14
Decrease speed to medium and add the eggs one at a time, beating well after each addition; pour the batter into the pan.
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15
Transfer the blackberry puree to a small glass measure; drizzle it in a spiral pattern over the batter, then swirl with a table knife through the batter to marbelize it.
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16
Bake for 55-60 minutes, until the cheesecake is puffed on the sides and still slightly jiggly in the center; let cool on a wire rack.
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17
Refrigerate the cheesecake, tightly covered, for at least 8 hours, until thoroughly chilled and set, of for up to 2 days.
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18
To serve, run a sharp knife around the edges of the pan to loosen the cake and remove the side of the pan.
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19
Cut the cheesecake into thin wedges with a sharp knife dipped into hot water and wiped dry after each cut.
