Cream together sugar and softened butter in a large mixing bowl until light and fluffy, about 3 minutes. Gradually beat in egg and vanilla extract.

Slowly add in flour and cornstarch, stirring until the dough forms and is smooth.

Preheat your oven to 350°F (175°C) and line a baking sheet with parchment paper.

Scoop tablespoonfuls of cookie dough onto the prepared sheet, spacing them about 2 inches apart.

Bake for 10–12 minutes, or until the edges are lightly golden. Allow to cool on a wire rack for about 15 minutes.

In a saucepan, combine milk and sugar, heating over medium heat until steaming.

Whisk together cornstarch with a few tablespoons of warm milk. Gradually whisk this back into the saucepan, stirring constantly until thickened, about 2–3 minutes.

Remove from heat, stir in vanilla extract, and allow to cool to room temperature.

Once cookies are cooled, spoon or pipe pastry cream into the center of each cookie, filling slightly over the sides.

Sprinkle granulated sugar over the pastry cream on each cookie. Using a kitchen torch, caramelize the sugar until golden and bubbly, about 30 seconds.

If using a broiler, place cookies on a baking sheet and broil for 1–2 minutes, watching closely.

Allow caramelized sugar to cool for a few minutes until crisp. Serve immediately or store in an airtight container.