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To make the topping: In a saucepan, combine the blueberries, 3/4 cup water, the cornstarch, lemon juice, and sugar and cook over low heat, stirring, for 5 minutes. Remove from the heat and let the topping stand to thicken. Set aside.
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To make the cheesecake: In a bowl, beat the cream cheese, sugar, and sour cream together until blended. In a separate bowl, whip the cream and vanilla extract until the cream just starts to thicken, 1 to 2 minutes. Add to the cream cheese mixture and beat for 30 seconds. Gently stir in the blueberries. Set aside.
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To make the crust: In a food processor or blender, grind the graham crackers into crumbs. Add the sugar and process until combines. Transfer to a bowl and add the butter and 3 tablespoons water, stirring until sticky. Refrigerate until needed.
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Pour the topping into each mold until it is one quarter full. Freeze for 2 hours.
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Pour the cheesecake mixture into each mold, leaving 1/2 inch at the top of each mold for the crust. Insert the stick. Freeze for 3 hours.
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Press the crust into the pop molds. If the crust is not sticking together, add more water. Freeze for at least 4 hours.
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Remove from the freezer; let stand at room temperature for 5 minutes before removing the pops from the molds.