Preheat oven to 375°F (190°C). Grease and line a 7-inch round cake tin with parchment paper.
In a large bowl, cream the butter and sugar together for about 2 minutes, until pale and fluffy. Scrape down the sides halfway through.
Beat in the eggs, egg yolks, and vanilla until combined.
In a separate bowl, sift together the flour, baking powder, and salt.
Add the dry ingredients to the wet mixture. Start mixing on low speed, then increase to medium and beat for 6 minutes until light and airy.
Stir in the caraway seeds, lemon zest, candied peel, and optional splash of brandy.
Transfer the batter to the prepared tin and smooth the top.
Bake for about 55 minutes, or until the top is golden and a toothpick inserted comes out clean.
Cool in the pan for 10 minutes before transferring to a wire rack. Store in an airtight container for up to 5 days.