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Combine the flour, butter and 1/3 cup of sugar in food processor or mixer.
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Mix until the dough is completely smooth.
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Line a 8x8 baking dish with parchment paper, then press the dough into the bottom of the dish into an even layer.
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Prick the dough with a fork several times, then bake at 350°F for 15-25 minutes, until the dough is lightly golden on the edges.
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Meanwhile, combine the cream cheese, eggs, sugar, sour cream and vanilla in a food processor or mixer, and blend until smooth.
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Once the crust is baked, pour the cheesecake mixture on top and smooth it out with a spatula.
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Pour a few lines of the passionfruit syrup on top, then swirl with a knife or toothpick.
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Bake the cheesecake bars at 325°F uncovered for 30-40 minutes, until the edges are slightly puffed and golden brown, but the center is just ever so jiggly.
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Refrigerate the cheesecake bars for 4 hours, or overnight.
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Once cooled, cut the bars into 9 squares for a generous portion, but you can also do 12-15 pieces for slightly smaller bites.