Heat your oven to 180°C (350°F) and prepare a loaf pan by greasing and flouring it.
Melt the butter in the microwave and let it cool.
In a mixing bowl, use an electric mixer to beat the eggs and caster sugar until they double in size and become lighter in color (about 3 to 5 minutes).
With the mixer on low, slowly add the melted butter, then mix in the vanilla extract and Greek yogurt until well combined. Use a spatula to scrape the edges if needed.
In another bowl, mix together the flour, baking powder, baking soda, and salt. Add this mixture to the wet ingredients in two parts, mixing on low speed each time. Just combine the ingredients; avoid overmixing to prevent the batter from deflating
Take half of the batter and put it in a separate bowl.
Add cocoa powder to the first bowl and gently mix until combined, using a spatula to scrape the edges if needed.
Pour small amounts of the vanilla and chocolate batters alternately into the loaf pan.
To create a marble effect, use a knife to zigzag through the batter in the pan without scratching it, mixing the two batters together.
Bake for around 35 to 40 minutes or until a skewer comes out clean.
Optional: For a clean crack in the center, take the pan out of the oven after around 10 minutes of baking, use a sharp knife to slash the center of the cake, and then put it back in the oven to finish baking.