Place a rack in middle of oven; preheat to 350ºF. Line 2 large baking sheets with parchment.
In a small bowl, whisk flours, baking soda, cardamom and salt. In a large bowl, using an electric mixer on medium-high speed, beat eggs and sugar until pale and thick, about 5 minutes. On low speed, gradually beat in flour mixture until just incorporated. Fold in nuts.
Divide dough in half and shape into 2 logs, each 12 inches long and 1 1/2 inches wide. Place on a baking sheet, 3 inches apart. Bake until firm and golden, about 25 minutes. Reduce oven to 300ºF. Place racks in top and bottom thirds of oven. Let baked logs cool for 10 minutes. Transfer 1 log to a cutting board. Cut with a serrated knife on a slight diagonal into 1/4-inch slices. Repeat with second log.
Lay slices on baking sheets. Bake, flipping slices and switching sheets halfway through, until crisp and dry, about 18 minutes. Transfer to wire racks to cool completely.