Set the butter in a skillet over low heat. Crush the cardamom seeds with a mortar and pestle until you have some large seeds but also some cardamom powder. Add it to the melting butter and turn off the heat. The residual heat from the pan should melt the rest of the butter. Set aside for 10 minutes so the cardamom flavor can be infused into the butter.
Once cool, zest the lemon (or orange, if you prefer) into the butter and stir to combine. Transfer the butter (along with everything added to it) to a medium sized mixing bowl.
Add the sugars (fine granulated and brown) to the bowl along with the salt and vanilla and whisk well, for 30 seconds.
Set the bowl in the microwave for 30 seconds, so the butter and sugar begin to melt together.
Whisk the mixture for another 30 seconds until the mix turns thick and shiny.
Add the egg and whisk until smooth. Add the flour, cornstarch, baking powder, and baking soda and switch to a rubber spatula. Stir until the cookie dough is smooth and there are no visible flour bits.
Cover the bowl with plastic wrap to seal and set in the fridge for at least an hour but up to 4 hours.
When ready to bake, preheat the oven to 350 F. Line two cookie sheets with parchment paper (grease them first so the parchment stays in place).
For the sugared topping: add cardamom seeds to the mortar again along with the sugar and pinch of salt. Use the pestle to crush the seeds into the sugar. Then sift the sugar to get rid of any big chunks. Alternatively just whisk together ½-1 teaspoon ground cardamom with the sugar.
Portion the cookies into 2 tablespoon scoops per cookie. Roll the cookie dough balls around the bowl of sugar to coat. Then place on the pan. Leave a lot of room around the cookies, these spread quite a bit.
Bake the cookies on the middle rack of the oven until they puff up and crack and the sides begin to turn golden brown, for about 12 minutes (less if your cookies are smaller).
Let the cookies cool on the pan before moving.