Preheat the oven to 350 degrees fahrenheit and prepare a baking sheet with parchment paper and set aside.
In a mixing bowl, or a stand mixer with the paddle attachment, beat the butter and sugar together until creamy.
Add the vanilla and lemon extracts and beat again.
Add the flour to the wet ingredients and mix together just until combined.
On the prepared parchment sheet roll out balls of dough about 1.5 inches round.
Slightly flatten each cookie with the palm of your hand.
Then use your thumb, or the back of a teaspoon, to press an indentation in each cookie to fill with lemon curd.
Put the lemon curd filling in a piping bag and cut the tip. Fill each hole in the unbaked cookies with lemon curd filling.
Place in the oven for 10-12 minutes or until the cookies are just starting to color around the edges.
While the cookies are in the oven, make the lemon icing by adding the powdered sugar, lemon juice and milk to a bowl and mixing together until smooth.
Transfer to a piping bag.
Once the cookies are out of the oven, snip the end of the lemon frosting piping bag and drizzle the glaze over all the cookies.
For extra flare and more lemon-y flavor zest a lemon over the top of all the cookies.
Notes
The lemon curd can be cooked or uncooked. Indent (thumbprint) the cookies before baking and fill with curd afterwards if you prefer. Both ways taste great!