Roll out the puff pastry, halve the dough lengthwise, then cut each half crosswise into approx. 9 strips. Slide onto a tray together with the baking paper, place a sheet of baking paper over the dough and weigh down with a second tray.
Bake for approx. 15 mins. in the centre of an oven preheated to 220°C. Remove from the oven, leave to cool on a cooling rack.
Blanch the basil in boiling water for approx. 30 secs., remove, dip briefly in ice-cold water, drain well. Puree the basil with the milk. In a pan, whisk the milk and all the other ingredients up to and including the egg yolks, bring to just below the boil over a medium heat, stirring constantly. Remove the pan from the heat immediately. Stir the gelatine into the hot custard, then pour the mixture through a sieve into a bowl. Stir in the lime zest, cover and leave to cool. Chill the custard until it is just set at the edges, stir until smooth, fold in 1 tbsp of lime juice and the whipped cream. Set aside the remainder of the lime juice. Transfer the custard to a piping bag with a smooth nozzle (approx. 12 mm in diameter), chill for at least 1 hr.
Place the remainder of the lime juice in a blending cup along with the honey and herbs, blend until smooth.
Pipe the custard onto 12 pieces of puff pastry, place two pieces on top of each other. Cover with the remaining pieces of puff pastry, drizzle with 3 tbsp of herb honey.