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To make the crust, preheat oven to 350 degrees F. Also preheat a rimmed baking sheet. Combine everything but the butter in the bowl of a food processor and process until the texture is consistent and gravelly. Drizzle in butter; pulse a few times. Using the flat bottom of a glass, press into a liberally buttered 9-inch tart pan evenly. Carefully set in the freezer for 15 minutes.
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Next, knock crumbs out of your food processor and wipe clean. Combine all of the filling ingredients and process for 30 seconds, until mixture is smooth. Pour into chilled crust, set on preheated baking sheet and bake 30 minutes, or until filling is set and the sides have puffed up slightly. Carefully set tart on a wire rack to cool.
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While cheesecake bakes, prepare topping. In a medium saucepan, combine lime juice, vanilla extract, and salt, and cook over medium-high heat. Gently add pears; cook over medium-high heat for 3 minutes. Pears will soften, but still hold their shape and a have bit of bite. Remove pears, turn heat to high and reduce remaining juices briefly, just until the liquid starts to change color. Pour syrup into a small bowl and set aside to cool.
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When tart has cooled completely, arrange the pears into a simple rosette in the center or scatter around the tart. Serve slices with a drizzle of pear lime syrup.