In a small bowl, combine the topping sugar and 1 teaspoon lemon zest. Rub them together with your fingertips until the sugar is fragrant and lightly tinted yellow; set aside.
Preheat the oven to 360°F. Line 2 baking sheets with parchment paper and set aside.
Whisk the flour, baking powder, baking soda, salt, and cardamom in a medium bowl until evenly combined.
In a large bowl, add the 1 cup sugar and 2 tablespoons lemon zest. Rub together well, then add the softened butter. Beat with an electric mixer on high until pale and fluffy, 1–2 minutes.
Beat in the egg and vanilla on medium speed until the mixture looks creamy and slightly thickened, about 1 minute. Scrape down the bowl.
Add the dry ingredients and mix on low just until the last streaks of flour disappear. Cover and chill the dough in the refrigerator for 15 minutes to make scooping and shaping easier.
Scoop the dough with a 2-tablespoon cookie scoop into 20 portions. Dip only the tops of each dough ball into the lemon sugar, then set on the prepared sheets, sugar-side up, spacing about 2 inches apart. Use a flat-bottomed glass dipped in the lemon sugar to gently press each mound to about 1/2 inch thick.
Bake one sheet at a time for 10–11 minutes, just until the edges are set and the centers look slightly soft. Let cookies rest on the hot sheet for 5 minutes.
While warm, lightly sprinkle a pinch of the remaining lemon sugar over each cookie for extra sparkle. Transfer to a wire rack to cool completely before serving.