In a medium bowl, combine the flour, cardamom, baking powder, baking soda, and salt. Stir with a whisk to blend. Set aside.

In a large bowl, cream the butter and sugar together until pale and fluffy. Beat in the lemon zest. Add the eggs, one at a time, beating well after each addition. Be sure to scrape down the sides of the bowl so everything gets mixed evenly. Mix in vanilla, buttermilk, and lemon juice. Slowly add in dry ingredients and mix until incorporated. Stir in white chocolate chips. The dough will be sticky. Cover bowl with plastic wrap and chill at least 1 hour or until firm enough to shape into balls.

Preheat oven to 350 degrees F. Line two cookie sheets with parchment paper, or a Silpat liner. Pour the granulated sugar and powdered sugar into separate shallow bowls. Lightly dust your palms with powdered sugar to keep the dough from sticking to your hands. Scoop out about two tablespoons of the dough for each cookie and gently roll into a ball. Roll the ball lightly in granulated sugar first, then roll heavily in powdered sugar. Place on the cookie sheet about 2 inches apart, as they will spread out while baking. Repeat with the rest of the dough.

Bake for 10-13 minutes until the bottoms of the cookies begin to brown and the cookies are no longer shiny. Remove from oven and let cool 2-3 minutes before transferring to a wire rack to cool completely. Store in an airtight container.