For the Cake:

1 cup (2 sticks) unsalted butter, at room temperature

1 cup granulated sugar

zest of 1 large lemon

4 large eggs, at room temperature

1 vanilla bean, seeds scraped and pod discarded (or 2 teaspoons pure vanilla extract)

2 cups all-purpose flour

2 teaspoons baking powder

1/4 teaspoon salt

1/4 cup fresh lemon juice

For the Buttercream:

1/2 cup (1 stick) unsalted butter, at room temperature

2 to 3 cups powdered sugar

2 tablespoons fresh lemon juice

1 teaspoon pure vanilla extract

splash of milk or cream as needed for consistency

1 tablespoon poppy seeds