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In a medium bowl, combine the gingersnaps, butter, and sugar. Press the crumb mixture firmly into a 9 x 13 baking pan. Set aside.
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In a large mixing bowl, beat the cream cheese until whipped and smooth. Add the orange rind, vanilla, and sugar, and continue beating. Finally add the eggs and beat until evenly mixed. Using a spatula, pour the batter into the prepared crust. Bake at 350 for 30 to 35 minutes, or until light golden brown. Remove from oven and cool on a wire rack. Then cover and chill the bars for at least 3 hours.
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Meanwhile, prepare the clementines: Break the peeled clementines into segments and set them out to "dry" at room temperature. The outer skin will become slightly dry and crackly while the inside will stay juicy. Once the cheesecake bars are chilled, cut into bite-sized pieces and top each piece with a clementine segment.