Preheat your oven to 350°F (175°C). Grease a loaf pan or round cake pan and line it with parchment paper for easy removal.
In a large mixing bowl, whisk the eggs and sugar together until light and frothy. Stir in the Greek yogurt and vanilla extract until smooth and well combined.
Sift the flour, baking powder (if using), and a pinch of salt into the wet mixture. Gently fold the dry ingredients into the wet mixture until just combined.
If desired, fold in extras like lemon zest, cinnamon, chocolate chips, or fresh berries.
Pour the batter into the prepared pan and smooth the top with a spatula. Bake for 30–35 minutes, or until a toothpick inserted into the center comes out clean or with a few moist crumbs.
Let the cake cool in the pan for 10 minutes before transferring it to a wire rack to cool completely. Slice and serve plain, dusted with powdered sugar, or topped with honey, jam, or fresh fruit.
