Preheat oven to 400°F (200°C). Line two baking sheets with parchment paper.

Unroll the thawed puff pastry sheet onto a lightly floured surface. Using a rolling pin, gently roll it a little thinner, to about 1/8-inch thick, to ensure even baking and crispiness.

Using a 2-inch (5cm) round cookie cutter, cut out as many circles as possible. Re-roll scraps gently if needed to get more circles, ensuring not to overwork the dough. You should get approximately 24-30 circles.

Carefully transfer the pastry circles to the prepared baking sheets, leaving a little space between them. Prick each circle several times with a fork to prevent excessive puffing.

Place a second sheet of parchment paper over the pastry circles and then another empty baking sheet on top. This helps to keep the pastry flat and creates crisp, even layers (mimicking mille-feuille style).

Bake for 15-20 minutes, or until golden brown and crisp. Remove the top baking sheet and parchment paper, and let the pastry cool completely on a wire rack.

In a small saucepan, combine raspberries, 1/4 cup granulated sugar, and 1 tbsp lemon juice. Cook over medium heat, stirring occasionally, until the raspberries break down and the mixture starts to bubble, about 5-7 minutes.

In a small bowl, dissolve 1 tsp cornstarch in 1 tbsp cold water to create a slurry. Stir the slurry into the hot raspberry mixture. Cook for another 1-2 minutes, stirring continuously, until thickened.

Remove from heat. For a smooth filling, press the mixture through a fine-mesh sieve to remove seeds. Set aside 1-2 tablespoons of the strained puree for the glaze. Let the remaining filling cool completely.

In a medium saucepan, gently heat 1/2 cup whole milk over medium-low heat until simmering.

In a separate medium bowl, whisk together egg yolks, 2 tbsp granulated sugar (from the 1/4 cup total), and 1 tbsp cornstarch until smooth and pale.

Gradually temper the hot milk into the egg yolk mixture, whisking constantly to prevent scrambling. Pour the mixture back into the saucepan.

Cook over medium-low heat, whisking continuously, until the custard thickens significantly and comes to a gentle boil for 1 minute. Remove from heat and stir in vanilla extract.

Transfer the custard to a clean bowl, cover the surface directly with plastic wrap to prevent a skin from forming, and chill completely in the refrigerator (at least 1 hour, or speed up in freezer for 15-20 min).

Once the custard is thoroughly chilled, whip the cold heavy cream with the remaining 2 tbsp granulated sugar in a stand mixer (or with a hand mixer) until stiff peaks form.

Gently fold the whipped cream into the chilled custard until fully combined and smooth. Transfer the diplomat cream to a piping bag fitted with a round tip.

Match the cooled puff pastry circles into pairs of similar size and shape.

On one half of the pastry circles, pipe a small dollop or ring of vanilla diplomat cream around the edge, leaving the center open.

Fill the center with about 1/2 teaspoon of the cooled raspberry filling.

Place a second puff pastry circle on top to create a sandwich. Repeat with all cookies.

In a small bowl, whisk together the sifted powdered sugar and the reserved 1-2 tablespoons of raspberry puree (and optional lemon juice) until a smooth, pourable glaze forms. Adjust consistency with more powdered sugar or a tiny bit more puree/water if needed.

Dip the top of each assembled cookie into the raspberry glaze, or drizzle the glaze artistically over the tops. Allow the glaze to set slightly.

Just before serving, place a halved fresh raspberry on top of each cookie and dust lightly with powdered sugar.