Preheat the oven to 350°F (175°C). Grease a loaf pan or line it with parchment paper.

In a large bowl, whisk together flour, sugar, baking powder, and salt until combined.

In another bowl, beat eggs and cream cheese until smooth. Mix in lemon zest, lemon juice, and vanilla extract.

Gradually combine the wet mixture into the dry ingredients, stirring gently until just combined.

Pour the batter into the prepared loaf pan and spread evenly.

Bake for 50-60 minutes or until a toothpick comes out clean. Cool in the pan for ten minutes before transferring to a wire rack.