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Place the mesh sieve over a medium bowl and set aside.
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In a medium saucepan, combine the cherries, sugar, and salt. Bring to a boil over medium high heat, stirring to dissolve the sugar. Reduce the heat to medium-low and let simmer until the cherries have softened and released their juices.
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Remove the saucepan from the heat and pour the mixture through the prepared sieve. Allow the cherries to drain.
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Pour the cherry juices back into the saucepan, leaving the cherries in the sieve over the bowl. Bring the juices to a bowl and then cook until the juices have reduced to ⅓ cup. Remove from the heat.
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Combine the cornstarch and the water in a small bowl, stirring until smooth. Whisk the cornstarch mixture into the juices and return the saucepan to the heat. Cook, stirring constantly, until the mixture is thick and glossy, about 5 minutes.
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Remove the mixture from the heat. Whisk in the cinnamon, lemon zest, and vanilla extract. Add the cherries and stir to combine. Refrigerate uncovered for 1 hour.