Preheat the oven to 350 degrees F. Set out 2 sheet pans.
Whisk to combine the flour, cardamom, baking powder, 1/2 teaspoon salt, and lemon zest in a large bowl and set aside.
Sift the powdered sugar into another bowl to ensure there are no lumps and set aside.
In an electric standing mixer fitted with the paddle attachment, spread the butter around the bowl by mixing on low for about 20 seconds. Bump the speed up to medium low, and slowly stream in the granulated sugar. Cream the butter and sugar on medium speed for about 2 minutes.
(We are cutting little holes in the butter with the abrasive sugar, and those little holes will expand from the leavening properties of the baking powder during baking so we can get that soft cakey texture for the cookies.)
Scrape down the bowl with a spatula, add the eggs one at a time, and mix on medium until incorporated. Add the vanilla and beat until blended.
Turn off the mixer and add the flour mixture. Mix on low speed until the flour disappears.
Use a number 40 (1 1/2 tablespoons) scoop to portion out your cookies, then roll the portioned dough into small balls. Roll the balls in the sifted powdered sugar, and place on the sheet pan at least 2-inches apart.
Bake for 13 to14 minutes, until the surface of the cookies have cracked and puffed up. The cookies will not be browned. Cool the cookies on a wire rack and serve.
Cook's Note: When you bite into these cookies, you first get through the gently crisp and sweet edge, and your teeth sink into the tender, soft, and cakey interior. These cookies have a unique flavor, as it is a combination of Meyer lemon (often described as a cross between lemon and orange) as well as ground cardamom.
Creaming the butter and sugar together is such an important step. This method ensures that the cakey tender texture characteristic of this cookie is achieved.