Unroll the puff pastry sheet and slice into 1 dozen squares. Use a rolling pin to thin the dough out a tiny bit. Tuck a square into each cavity of a mini muffin tin. Bake as directed on package. Remove from oven and allow to cool.
Make the Cherry Sauce. In a medium saucepan, bring the cherries, sugar and water to a boil over medium-high heat, stirring frequently. Stir the lemon juice and cornstarch together in a small bowl until smooth. Whisk it into the cherry mixture. Return the whole thing to a boil, stirring constantly. Keep cooking until the liquid has thickened. Should take about 1 minute.
Remove from heat. Taste the sauce carefully and add a bit more sugar if needed and stir well. Set the sauce aside to cool to room temp.
Make the Key Lime Cheesecake Mixture. Using an electric mixer, beat the cream cheese and sugar on medium-high until creamy and completely combined. Pour in the heavy cream, lime juice and lime zest. Beat until completely combined and thick. Set aside.
Once everything is cooled to room temp, remove the puff pastry shells from the muffin tin and place on a platter. Using a piping tool or a baggie with a tip cut off, pipe the lime cheesecake mixture into each puff pastry cup. Top with Cherry Sauce.
Top each puff pastry with a beautiful, fresh cherry.
Place in the refrigerator to chill until firm, at least 4 hours. I usually do overnight but 4 hours is good. Serve chilled.