Preheat your oven to 350°F (175°C). Grease and flour two 9-inch round cake pans.
In a mixing bowl, cream together the butter and sugar until light and fluffy. Add the eggs one at a time, beating well after each addition. Stir in the vanilla extract.
In another bowl, whisk together the flour and baking powder. Gradually add the dry ingredients to the wet mixture, alternating with the milk, beginning and ending with the flour mixture. Mix until just combined.
Divide the batter evenly between the prepared cake pans. Bake for 25 minutes or until a toothpick inserted into the center comes out clean. Let the cakes cool in the pans for 10 minutes, then turn them out onto a wire rack to cool completely.
For the Meyer lemon curd, whisk together the lemon juice, sugar, and eggs in a saucepan over medium heat. Cook, stirring constantly, until the mixture thickens and coats the back of a spoon. Remove from heat and stir in the butter until melted and smooth. Let cool completely.
To assemble the cake, place one layer on a serving plate and spread with half of the lemon curd. Top with the second layer and spread the remaining lemon curd on top. Serve and enjoy!