For the lemon cream, bring the double cream to the boiling point in a heavy-based saucepan. Immediately reduce the heat until the mixture is simmering.
Add the sugar, stir well, then continue to simmer for 2-3 minutes, stirring regularly, until the mixture has thickened and the sugar has dissolved.
Add the lemon juice and zest and continue to simmer for 30 seconds, stirring continuously. Remove from the heat and set aside to cool slightly for 10 minutes.
When the cream mixture has cooled slightly, pour it into four tall serving glasses. Set aside until completely cool, then chill in the fridge for at least two hours.
Meanwhile, for the berry compôte, heat the berries and sugar in a pan, stirring well, and bring to a simmer. Continue to simmer for 4-5 minutes, or until the sugar has melted and the berries have broken down, then remove the pan from the heat and set the mixture aside to cool.
To serve, spoon the berry compôte over the chilled lemon cream. Place each serving glass and one piece of shortbread onto a plate. Serve with long-handled spoons.