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Combine the cream cheese and sugar in a medium mixing bowl and beat with an electric mixer on medium until very smooth.
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Add the flour and beat on low to combine; scrape down the sides and bottom of the bowl.
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Beat in the eggs one at a time, then beat in the sour cream, vanilla, almond extract, lemon zest (if using), and salt. Scrape down the sides and bottom of the bowl, then beat on low for a few more seconds.
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Spread the filling over the crust. Dollop the cherry puree over and swirl a bit with a butter knife, taking care not to disturb the crust.
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Return the pan to the oven for 30 to 40 minutes, until the edges of the cheesecake are set but the center still jiggles.
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Remove from the oven and run a knife around the edge of the pan. Set the pan on a wire rack to cool completely, then chill for at least 4 hours (or overnight). Use the foil to remove the bars from then pan, then slice and serve.