Adjust two oven racks to sit in the middle positions. Preheat the oven to 375°F (190°C). Prepare two baking trays by lining them with parchment paper or silicone baking mats.

In a mixing bowl, combine the softened cream cheese, granulated sugar, egg yolk, lemon juice, and vanilla extract. Beat together on medium-low speed until the mixture is fully blended and smooth.

If using homemade puff pastry, dust your work surface lightly with flour and roll the dough into a rectangle measuring 16 inches by 8 inches. Divide the sheet lengthwise, then cut crosswise into four equal parts, yielding eight 4-inch squares. For pre-packaged sheets, gently roll to smooth any fold lines before cutting into eight squares of similar size.

Use a pastry brush to apply a light coat of the beaten egg white around the edges of each square. Fold each corner inwards by about an inch toward the center, pressing gently so they adhere. Arrange the shaped squares on the lined baking trays, ensuring 2 inches of space between them. Brush any uncovered dough with more egg white.

Place roughly 1 tablespoon of the cream cheese mixture into the center of each folded square.

Transfer the trays to the oven and bake for 15 minutes. Afterward, rotate the pans and continue baking for an additional 15 minutes, or until the pastry is puffed up and golden in color. Let the danishes rest on the baking sheets while you prepare the glaze.

To make the glaze, whisk together the powdered sugar, milk, and vanilla extract until the mixture becomes smooth and pourable. Drizzle generously over the pastries once they are warm but no longer hot.