In a heatproof bowl, whisk together sugar and egg yolks. Place the bowl over a saucepan of simmering water (double boiler) and whisk constantly until thickened and pale yellow, about 5-7 minutes. Remove from heat.
In a small saucepan, heat milk until just simmering. Gradually whisk the hot milk into the egg yolk mixture. Return the mixture to the saucepan and cook over low heat, stirring constantly, until it thickens enough to coat the back of a spoon. Do not boil.
Remove from heat and stir in the chopped white chocolate until melted and smooth. Let the mixture cool slightly.
In a separate bowl, beat the softened mascarpone cheese until smooth. Gently fold the slightly cooled white chocolate mixture into the mascarpone. Then, fold in the whipped heavy cream until just combined.
Quickly dip each ladyfinger into the raspberry liqueur. Arrange a layer of dipped ladyfingers in the bottom of a 9x13 inch dish.
Spread half of the mascarpone mixture over the ladyfingers. Scatter half of the fresh raspberries over the mascarpone layer.
Repeat the layers: dip and arrange another layer of ladyfingers, spread the remaining mascarpone mixture, and scatter the remaining fresh raspberries.
Cover the dish with plastic wrap and refrigerate for at least 4 hours, or preferably overnight, to allow the flavors to meld and the ladyfingers to soften.
Before serving, garnish with white chocolate shavings.
Notes
For a non-alcoholic version, you can use raspberry juice or a simple syrup infused with raspberry flavor.