Add the cream, sugar, lime zest and lemongrass (if using) to a pan and place over a moderate to high heat. Boil the cream for 1½ minutes, stir in the lime juice, bring back up to the boil and immediately remove from the heat.
Strain the cream through a sieve and pour into four glasses. Refrigerate for at least 1 hour before serving.
Meanwhile dice or slice the strawberries and add to a bowl. Add freshly ground black pepper to taste (the strawberries can take quite a bit, at least ½-1 tsp). Leave to macerate for at least 30 minutes, then add 1 tsp, or more to taste, of caster sugar if you think the strawberries need it.
Serve the possets with the black pepper strawberries.