Make the lemon curd according to the recipe and let it fully cool and set before using.
Add the butter, powdered sugar, vanilla, and flour to a bowl and knead into a firm dough. Wrap in plastic wrap and refrigerate for at least 1 hour.
Lightly grease a mini muffin pan. Cut narrow strips of parchment paper and place them into each cavity, this will help lift out the cookie cups later.
Divide the dough into 14 pieces. Roll each into a ball, then press into the muffin cups to form a cup shape. Trim excess dough and prick the bottoms with a fork.
Bake at 350°F (175°C) for 14-16 minutes until golden brown.
The centers will puff up slightly while baking. While still warm, use a spoon or the end of a wooden spoon to gently press the centers back down.
Let cool completely, then fill each cookie cup with about 1 teaspoon of lemon curd.
Whip the cream with the vanilla sugar until stiff, transfer to a piping bag (I used a 1M tip), and pipe a swirl on each cookie.