For the semifreddo
Put 2 tablespoons water into a cup, sprinkle in the gelatin, and set aside to soften and swell, 3 to 5 minutes. Pour the milk into a small saucepan. Split the vanilla bean and scrape the seeds into the milk. Add the bean and bring the milk just to a boil over high heat. Remove from heat, discard the vanilla bean, add the softened gelatin, and whisk to dissolve the gelatin. Strain through a fine sieve into a small bowl.

Put the white chocolate into a large bowl (saving some to shave for garnish). Slowly pour the hot milk over the chocolate, stirring constantly until the chocolate has melted. Set aside and allow to cool to room temperature.

Put the cream into a mixing bowl and beat until it forms soft peaks. Mix the lemon zest and juice into the cooled milk mixture, then fold in the whipped cream. Pour into a mold of whatever shape you prefer — rectangular or square — and freeze until set.

For the berries
While the semifreddo is in the freezer, make the vanilla-poached berries. Put 1/2 cup water, the sugar, lemon zest, and split vanilla beans into a sauce pan and boil for 5 minutes over medium-high heat, until the sugar has dissolved. 

Add the blueberries and blackberries, reduce heat to low, and poach for 2 minutes. Remove from heat and add the strawberries. Let cool, then refrigerate.

For the lemon cookies
Put the powdered sugar, ground almonds, and salt into a mixing bowl. Beat the butter in the bowl of a standing mixer fitted with a paddle until pale yellow and fluffy. Add the eggs, lemon zest, and sugar mixture and continue beating. Slowly add the flour while beating, until it is just incorporated. Wrap the dough in plastic wrap and refrigerate for 30 minutes to an hour before rolling out.

Preheat the oven to 325˚F. Sprinkle a work surface with a little powdered sugar and roll out the dough to a thickness of 1/8 inch. Cut 1 large cookie just the size of the semifreddo and cut the remaining dough into 6 small rounds. Place the cookies on a cookie sheet and bake until golden brown, 20-25 minutes. Cool.

To serve
Unmold the semifreddo and carefully place it on top of the large cookie. Slice into 1-inch pieces and serve each slice with a generous spoonful of the poached berries, mint leaves, shaved white chocolate on top, and an extra lemon cookie on the side. Add a white chocolate cigarette, if you like.