Crack the cardamom pods open by squashing them gently using a pestle and mortar, or with the end of a rolling pin. Put the cream and cracked cardamom pods in a pan, heat gently, bubbling for 1-2 mins, then set aside to infuse for at least 2 hrs or, if you have time, cool then chill overnight.
Roll out the pastry to the thickness of a £1 coin, then use to line a 23cm loose-bottom, fluted tart tin. Snip off most of the excess pastry with a pair of scissors, leaving about 2cm overhanging. Chill for 30 mins.
Heat oven to 200C/180C fan/gas 6 and place a baking sheet on the middle shelf. Remove the tart case from the fridge, line with baking parchment or foil, and fill with baking beans. Place on the baking sheet and bake for 15 mins, then remove the parchment or foil and beans, and return the case to the oven for a further 10 mins until cooked through and starting to turn golden around the edges. Remove from the oven and, while the pastry is still warm, use a small serrated knife to slice off the excess pastry. Set aside to cool a little while you prepare the filling.
Reduce oven to 140C/120C fan/gas 1. Chop the chocolate into small pieces and place in a large bowl. Whisk the eggs and sugar in another bowl. Measure the cardamom-infused cream and top back up to 300ml with a splash of extra cream. Pour back into the pan and warm through on the hob until just steaming, but not boiling, then strain onto the chopped chocolate, discarding the cardamom pods. Leave to stand for a few mins, then stir until smooth and glossy. Add the warm chocolate cream to the eggs, whisking as you go, until combined. Pour into the tart case, then carefully slide into the oven. Bake for 30 mins until just set (the filling should still have a wobble), then remove and chill for at least 2 hrs, or overnight.
Place the freeze-dried raspberries in a mortar, and crush with a pestle to a dusty texture. To serve, scatter the raspberry dust over the tart. Serve in slices with fresh raspberries on top and a jug of cream on the side.