Nigel Slater's The Kitchen Diaries has a recipe for lemon iced pistachio and almond cake that looks (there's a picture in the book) and sounds delicious. It's not a light sponge, but should be lovely with a bit of whipped cream.
The recipe flavourings are rosewater and orange, but I don't see why you couldn't leave those out and add cardamom, which would be gorgeous.
250 g butter
250 g sugar
3 eggs
100 g each shelled pistachios and ground almonds
60 g plain flour
1 teaspoon rosewater
one orange
Cream the butter and sugar until very light, then add the eggs one at a time, beating between each addition. Blitz the pistachios to a powder then fold them and the ground almonds into the butter and sugar mix.
Grate the zest and squeeze the juice of the orange into the mix and rosewater if using (or the cardamom), then fold in the flour.
Spoon the mixture into a baking parchment lined 22 cm tin and smooth the top. Bake at 160C for 50 minutes, covering the top with foil for the last ten minutes. A cake tester should come out clean, with no wet mixture sticking to it.
Leave the cake in the tin until thoroughly cooled then turn it out. If you'd like you can add a drizzle icing made with 100 g icing sugar and the juice of two lemons.
I haven't made this (no pistachios, no oranges, no flour) but it's on my list when I do get supplies in. The aroma of pistachios and cardomon would be enticing.