Preheat the oven to 400°F and line a baking sheet with parchment paper. Place the cottage cheese in a fine-mesh strainer and let it drain for 10 minutes, pressing gently with a spoon to remove excess liquid.
Add the drained cottage cheese, cream cheese, powdered sugar, egg yolk, cornstarch, vanilla extract and lemon zest to a blender. Blend until thick and completely smooth.
Unfold the puff pastry on a lightly floured surface and cut it into 6 rectangles. Transfer them to the baking sheet.Prick the center of each rectangle several times with a fork, leaving a 1/2-inch border untouched. This keeps the center flat while the edges puff up around the filling.
Brush the borders with beaten egg. Spoon about 2 tablespoons of the cottage cheese filling onto the center of each pastry, then top with a spoonful of cherry pie filling.
Bake for 18 to 20 minutes, until the pastry is puffed and deep golden and the filling is set.
Let the danishes cool for 10 minutes. Whisk the powdered sugar with enough milk to make a thick, pourable glaze and drizzle it over the pastries.