Combine cherries, water, lemon juice, sugar and cornstarch in a small sauce pan. Bring the cherry mixture to a boil over medium-high heat; reduce the heat to low. Cook, stirring frequently, about 5 to 10 minutes. The cherry sauce will start to thicken significantly. Turn off heat and stir in almond extract. Allow the filling to cool while thawing the pastry dough, at room temperature, about 45 minutes to 1 hour.
Preheat oven to 400 degrees.
Roll out the thawed pastry dough on a lightly floured surface, into a 9 x 12 rectangle. Cut the dough in half lengthwise, then cut each half into thirds. Using a pastry wheel or small knife, score a border ½ inch around the edge of each rectangle.
In a small mixing bowl, stir together the softened cream cheese, sugar, and vanilla. Spoon 2 to 3 tablespoons of cream cheese mixture into the middle of each piece of dough. Spread the cream cheese evenly, trying to make sure the mixture stays within the borders.
Spoon 5 to 7 cherries into the middle of the cream cheese with some of the cherry juice.
Bake for 15 to 20 minutes, on the middle rack in the oven.
Remove the danishes from the baking sheet with a spatula and place onto a wire cooking rack to cool.
When the danishes are cool, Combine the powdered sugar, milk and vanilla extract in a bowl and whisk until smooth. Drizzle over the danishes or use a piping bag for a more decorative touch.
Serve warmed in the microwave or at room temperature.
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