Preheat your oven to 350°F (175°C) and grease a bundt pan.
Cream the softened butter and sugar together until light and fluffy.
Add the eggs one at a time, mixing well after each addition.
In a separate bowl, whisk together the flour, baking powder, and salt.
Gradually add the dry ingredients to the butter mixture, alternating with the milk.
Stir in the lemon zest, lemon juice, and vanilla extract until well combined.
Pour the batter into the prepared bundt pan.
Bake for 60 minutes or until a toothpick comes out clean.
Let the cake cool for 10 minutes in the pan, then invert onto a wire rack.
Allow the cake to cool completely before slicing.