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Preheat the oven to 300 degrees. Line 16 to 18 muffin cups with cupcake liners and set one sandwich cookie in the bottom of each. Set pan aside.
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Place the sliced berries in the bowl of a food processor and process until liquid. If your food processor has a small bowl, use that; if not, just keep stopping the processor and scraping it down until the berries are fully pureed.
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Pour the puree into a fine mesh sieve set over a mixing bowl and use a rubber spatula to press as much liquid out as possible. Discard solids. Stir 1 tablespoon sugar into the puree. Set aside.
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Beat the cream cheese with an electric mixer set to medium speed until very smooth. Turn mixer to low and slowly add the remaining 1/2 cup of sugar.
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Beat in the vanilla, eggs, sour cream, and salt stopping the mixer to scrape down the sides and bottom of the bowl as necessary.
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Divide batter evenly between the prepared muffin cups, filling each most of the way full.
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Spoon about 1 1/2 teaspoons of the strawberry puree over the top of the batter in each muffin cup and use a toothpick to swirl the puree into the cheesecake.
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Bake until filling is set, about 18 to 20 minutes. Set pan on a wire rack to cool completely, then refrigerate overnight.