Preheat oven to 350°F (175°C). Grease a 12-cup muffin pan or a 24-cup mini muffin pan.
Cookie: In a mixing bowl, combine butter and sugar, beating until well combined. Add the egg and vanilla extract, beating until incorporated. Add in the flour and baking powder, mixing until fully combined. The dough will be soft but not sticky. Chill the dough for 10 minutes if needed. Using a small cookie scoop, fill each cup with cookie dough and press down to create a cavity. Bake for 10-12 minutes. Allow to cool for 10-15 minutes before removing from the pan and transferring to a cooling rack.
Lemon Curd: Using a double boiler, combine lemon juice, lemon zest, eggs, egg yolk, and sugar in the top of the double boiler. Whisk constantly until the mixture thickens, about 10 minutes. Remove from heat and add butter, stirring until fully incorporated. Pour the curd into a glass jar, cover, and let cool for 15 minutes before refrigerating overnight or until set. You can make the curd the night before or use store-bought lemon curd.
Meringue: While the cookies cool, whisk egg whites, sugar, and cream of tartar over a double boiler until the sugar dissolves. Transfer to a stand mixer with a whisk attachment and beat on high speed for 6 minutes until stiff peaks form. Add vanilla extract.
Assemble: Using a piping bag, pipe lemon curd into each cookie cup. Top with piped meringue. Optionally, dust with powdered sugar and use a kitchen torch to lightly brown the meringue.