Preheat the oven to 350°F. Line two cookie sheets with parchment paper.
2. Step
In a large mixing bowl, beat the butter at high speed until creamy and smooth. Add the sugar and beat at medium speed until light and fluffy, scraping the bowl as needed.
3. Step
Add the egg, cardamom, and lemon zest and beat at medium low speed until thoroughly mixed. Slowly add the flour at low speed, to prevent mess. Mix until soft dough forms.
4. Step
Form 1 tbsp-sized dough balls and place 2-3 inches apart on the baking sheet.
5. Step
Bake for 25 minutes or until golden brown and slightly loose.
6. Step
To make glaze, whisk together powdered sugar and milk.
7. Step
Add the lemon juice, lemon zest, and vanilla extract and whisk until fully combined. The texture should be thin.
8. Step
After baking, take the cookies out of the oven and let cool on a baking rack for 10 minutes.
9. Step
After cooling, dip the top of each cookie face forward into the glaze and top with lemon zest.