How to Make It
In a saucepan, simmer the water with 1/2 cup of the sugar until the sugar is dissolved. Add the rosemary and the vanilla bean and seeds and let stand for 2 hours.
Meanwhile, in a heatproof bowl, rub the lemon zest into 1 cup of the sugar. Whisk in the eggs and lemon juice. Set the bowl over a saucepan of simmering water and cook over moderate heat, whisking, until thickened, about 6 minutes. Strain the custard into a food processor; let cool slightly.
With the processor on, add the butter 1 piece at a time and process until fully incorporated before adding more. Process the cream until doubled in volume, about 3 minutes. Scrape the cream into a bowl, press a piece of plastic wrap directly onto the surface and refrigerate until chilled, about 2 hours.
Discard the rosemary and vanilla bean from the syrup. Simmer the syrup over moderately low heat until slightly thickened, about 15 minutes; let cool.
Preheat the broiler. Arrange the brioche slices on a baking sheet and broil for 1 minute, turning once, until golden.
In a bowl, beat the heavy cream with the remaining 1 tablespoon of sugar until softly whipped. Add the blackberries to the sugar syrup and toss gently. Spoon the lemon cream onto 8 plates, top with the brioche and a dollop of the whipped cream. Scatter the blackberries on top; serve at once.