Preheat the oven to 180°C (350°F) and grease a 20cm (8-inch) round cake tin.
In a bowl, combine the grated courgettes, lemon zest, and thyme leaves.
In another bowl, whisk together the flour, baking powder, and salt.
In a separate large bowl, beat the sugar, melted butter, eggs, and vanilla extract until well combined.
Gradually add the dry ingredients to the wet ingredients, mixing well after each addition.
Stir in the courgette mixture and Greek yogurt until evenly incorporated.
Pour the batter into the greased cake tin and smooth the top with a spatula.
Bake for 45 minutes, or until a toothpick inserted into the center comes out clean.
Allow the cake to cool in the tin for 10 minutes, then transfer it to a wire rack to cool completely.
Serve and enjoy!