Whisk together the flour, cornstarch, baking powder, baking soda, and the salt in a mixing bowl. Whisk together the sugar, melted butter, egg and the milk in another mixing bowl, till well mixed.
Pour the wet mixture into the dry ingredients and whisk together until well mixed an smooth. Mix in the lime juice and then fold in the lime zest and the thyme.
Pour the batter into an 8” round cake tin that is grease and lined with parchment at the bottom. Bake at 180C (350F) for about 30 minutes till the cake is one and a skewer inserted into the middle of the cake comes out clean.
Let the cake cool in the tin for about 10 minutes. Then gently unmould the cake at let it cool completely before icing.
Make the Lime Icing.
Do while the cake is baking. Put the butter in a mixing bowl and with an electric mixer, beat till it is fluffy. Add the icing sugar in two or three batches an beat in till smooth. Beat in the vanilla extract, milk and lime zest so you have a smooth icing that’s on the runnier side than firm texture. You do not want a watery icing though. You won’t be able to pipe it but it should spread well without dripping off the side.
If the Icing feels too soft let it sit in the friged for about 15 minutes. Spread it over the top of the cool Lime & Thyme Cake and garnish with fresh thyme sprigs. Serve.