Preheat oven to 350°F (175°C) and line a baking sheet with parchment paper.
In a large bowl, cream together 1 cup softened butter and 1 cup sugar until light and fluffy, approximately 3 minutes.
Beat in 1 egg and 1 teaspoon vanilla extract until well combined.
Whisk together 2.5 cups flour, 0.5 teaspoon baking powder, and 0.25 teaspoon salt; gradually mix into the wet ingredients until a soft dough forms.
Scoop 1/4 cup portions of dough, roll into balls, and place on the baking sheet, flattening slightly to 1-inch thickness.
Bake for 10 to 12 minutes until the edges are set; do not allow the cookies to brown. Cool completely.
To make the curd, whisk 0.75 cup sugar, 2 eggs, and 0.5 cup lemon juice in a small saucepan over medium-low heat.
Stir constantly until the mixture thickens and coats the back of a spoon, then remove from heat and whisk in 4 tablespoons cubed butter and zest.
Transfer curd to a bowl, cover with plastic wrap touching the surface, and refrigerate for at least 1 hour until set.
Once cookies and curd are cold, spread a generous layer of curd over each cookie and finish with a dusting of powdered sugar.