Peel, core and roughly chop the apples. Do this as quickly as possible so that the apples don't have time to oxidise and turn brown.
Place in a pan small pan. Sprinkle the sugar and cinnamon over the top then add the butter. Bring to the boil, then simmer gently for a five minutes or so until soft. Take off the heat and allow to cool.
Set the oven to 160℃ (140℃ fan, 320℉, Gas 3).
Remove the leaves from the thyme sprigs and chop if they're particularly large.
Extract the seeds from the cardamom pods, if using. Grind them to a powder with a pestle and mortar.
In a large bowl, cream the butter together with the sugars, thyme leaves and cardamom, if using. A wooden spoon is best for this, although you can use an electric mixer if you prefer. Keep going until the mixture is pale in colour and fluffy in texture.
Beat in the eggs, one by one.
Sift in the flour, baking powder and cinnamon and stir until just combined.
Stir in the cooked apples until just combined.
Scrape the batter into a deep lined 20cm cake tin and bake for 50 minutes or until an inserted skewer comes out clean. If the top looks like it's getting too brown, cover with a sheet of parchment or brown paper
Allow to cool in the tin for ten minutes, then turn out onto a wire rack to cool completely.
Mix the icing sugar and cinnamon together, then dust over the top of the cooled cake.
