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First prepare the raspberry compote that gets swirled through the cheesecake. Bring the raspberries, sugar and 4 tbsp water to a gentle boil and then thicken with a slurry made by mixing together the cornstarch and 2-3 tbsp water.
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Boil only for an additional half minute or so, stirring constantly until the mixture completely thickens. Set aside to cool.
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Beat together the cream cheese, 1 cup sugar and vanilla extract until smooth
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Add the eggs one at a time.Beat well after each added egg.
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Blend in the 1/2 cup whipping cream.
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Stir in the raspberry puree.
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Pour into a 10 inch ungreased spring form pan that has the bottom lined with parchment paper.
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Drop tablespoonfuls of the raspberry compote, evenly spaced apart, onto the cheesecake batter. Using the handle of a wooden spoon, swirl the raspberry compote through the cheesecake batter. Bake for 60-70 minutes at 300 degrees F until the center sets. Cool to room temperature and then for a couple of hours in the fridge until completely cool, leaving it in the spring form pan while it cools.