Position an oven rack in the upper third of the oven and a second oven rack in the lower third of the oven. Preheat the oven to 375°F. Line 2 baking sheets with parchment paper.

In a medium bowl, toss the strawberries with 2 tablespoons of the granulated sugar and 1 tablespoon of the lemon juice. Allow the mixture to sit at room temperature until ready to use.

Meanwhile, in a stand mixer fitted with the paddle attachment, beat the cream cheese on medium speed until smooth, about 1 minute. Add the lemon zest and remaining ⅓ cup granulated sugar and beat until creamy, 2 to 3 minutes. Beat in the egg yolk and vanilla until well combined, about 1 minute.

On a lightly floured surface, unfold 1 sheet of the thawed puff pastry. Roll the sheet into a 12-by-8-inch rectangle, trimming as necessary. Cut the sheet in half lengthwise to create 2 (12-by-4-inch) strips. Cut each strip into thirds crosswise to form 6 (4-inch) squares, trimming to size. Place the squares on one of the prepared baking sheets.

Brush the edges of each square with the beaten egg. Fold each corner in about 1 ½ inches towards the center and press to adhere. Use a fork to prick the center of the pastry 3 to 4 times. Brush with more egg wash. Cover and refrigerate the squares while you repeat the process with the remaining puff pastry sheet.

Bake the squares until puffed, dry, and very lightly golden, 10 to 12 minutes.

Meanwhile, drain the strawberries. Return them to the bowl and toss them with the cornstarch.

With the back of a spoon, gently press down the centers of the pastry squares that may have puffed up high during baking. Scoop about 2 tablespoons of the cream cheese mixture into the center of each pastry; use a knife to smooth it. Top the cream cheese with a few strawberries.

Bake until the puff pastry is golden brown, 25 to 30 minutes, rotating the pans and swapping them between the top and bottom racks after 20 minutes. Allow the pastries to cool for 5 minutes on the baking sheets before moving them to a wire rack.

In a medium bowl, whisk together the powdered sugar and the remaining 1 teaspoon lemon juice until smooth and thick. Add additional powdered sugar, 1 tablespoon at a time, or water, 1 teaspoon at a time, until a thick, pourable consistency is reached.

Drizzle the danishes with the lemon glaze.