Preheat the oven to 350°F and line 2 cookie sheets with parchment paper.
In the bowl of a stand mixer fitted with the paddle attachment, cream together the softened butter and granulated sugar until light and fluffy. This takes about 2-3 minutes.
Add the eggs, one at a time, beating well after each egg.
Add the lemon zest, lemon juice, lemon extract and vanilla extract. Beat well until fully incorporated. The dough will look curdled, it's normal.
Add the baking powder, salt, all purpose flour and poppy seeds. Mix in on low speed just until fully combined.
Using a ⅓ cup or large cookie scoop, make 12 even cookie scoops and place 6 on each cookie sheet. Roll the cookie dough into smooth balls and flatten slightly with the palm of your hand so they look like thick hockey pucks.
Bake cookies one pan at a time on center rack for 14-16 minutes until edges are barely golden brown and the centers no longer look wet and glossy.
Let cookies cool on pan for 5 minutes then transfer to a wire rack to cool completely. Once the cookies are completely cooled, in a medium bowl whisk together the icing ingredients: powdered sugar, lemon extract and water until smooth. Start with 1 tablespoon of water and add more if needed to reach desired consistency.
Dip the top of the cookies in the icing or spread icing on top of the cookies with the back of spoon or an offset spatula. I prefer dipping them, it's faster and leaves the icing a lot smoother.
Place cookies back on wire rack and let rest until the icing is fully set.