Mix the cream cheese, sugar, vanilla, and cornstarch in a small bowl until smooth and thick. Scoop 24 small mounds, about 1 to 1½ teaspoons each, onto a parchment-lined tray and flatten them slightly into small discs. Freeze for 45 to 60 minutes, until firm enough to handle. The filling needs to be properly firm before it goes anywhere near the dough; soft filling will leak out during shaping instead of staying a defined center.

Cook the raspberries, sugar, and lemon juice in a small saucepan over medium heat for 4 to 6 minutes, stirring and lightly crushing the berries, until juicy. Mix the cornstarch with the water to make a slurry, stir it in, and cook another 1 to 2 minutes until thick and jammy. Transfer to a bowl and cool completely. The mixture should be thick, not runny; a loose filling will make the cookies spread more and raises the risk of a blowout, so cook it a little longer if it still looks wet.

Beat the butter with the brown sugar and granulated sugar until creamy and well combined, about 2 to 3 minutes. Beat in the egg, egg yolk, and vanilla until smooth, scraping the bowl well. In a separate bowl, whisk together the flour, cornstarch, baking soda, baking powder, and salt, then add this to the wet ingredients and mix just until combined before folding in the white chocolate chunks. The dough should be soft but thick; if it feels unusually loose, chill it for 15 to 20 minutes before assembling.

Line two trays with parchment and portion the dough into 24 pieces, about 40 to 45 g each. Flatten one portion into a disc, place one frozen cheesecake disc in the center, top with about 1 teaspoon of cooled raspberry mixture, then cover with a flap of dough or pull the dough around the filling and seal well. Don't fully blend the raspberry into the dough; a few visible streaks and pockets are what you want. Roll gently into a ball and place on the tray, pressing 1 to 2 extra white chocolate chunks and a small dab of raspberry mixture onto the top if you want a more visible finish. Repeat with the remaining dough, sealing each one completely around the cheesecake center and pinching closed any seam where cream cheese shows through.

Chill the assembled dough balls for 20 to 30 minutes. This helps the cookies bake thicker, keeps the cheesecake center in place longer, and reduces over-spreading.

Heat the oven to 175°C conventional or 160°C fan and line baking sheets with parchment. Space the chilled dough balls on the trays, about 6 per tray, and bake for 12 to 14 minutes, until the edges are golden, the tops are puffed and lightly crackled, and the centers still look a little soft. Don't overbake; the cookies should look slightly underdone in the middle when they come out, since they continue setting as they cool. For rounder cookies, swirl a round cutter or bowl gently around each one immediately after baking while still hot.

Let the cookies cool on the tray for 10 minutes before transferring carefully to a wire rack. The cheesecake centers stay very soft while hot, so avoid moving the cookies too early. For the cleanest creamy center, let them cool until just warm before breaking one open.