Preheat oven to 350°F (180°C). Line 2 rimmed baking sheets with parchment paper.

In the bowl of a stand mixer fitted with the paddle attachment, beat butter and sugars until fluffy, 3 to 4 minutes. Add eggs, one at a time, beating until combined after each addition. Beat in vanilla.

In a medium bowl, whisk together flour, baking powder, salt, cardamom, and baking soda. With mixer on low speed, gradually add flour mixture to butter mixture, beating until combined. Add white chocolate and finely crushed cereal, and beat until combined.

In a small shallow bowl, place roughly crushed cereal.

Using a 2-tablespoon spring-loaded scoop, scoop dough (about 53 grams each), and roll into balls; roll in cereal. Place about 1½ inches apart on prepared pans.

Bake until slightly domed and thick and edges are golden brown, 10 to 11 minutes. Let cool on pans for 5 minutes. Remove from pans, and let cool completely on a wire rack. Store in an airtight container for up to 5 days.