Preheat oven to 410°F. Line two baking sheets with parchment.
Toast walnuts on a sheet for 6 minutes until fragrant; cool, then chop.
Whisk all-purpose flour, cake flour, cornstarch, baking powder, baking soda, and salt.
Beat cold butter with both sugars until just creamy, about 60 seconds.
Mix in eggs and vanilla on low until combined; do not overbeat.
Add dry ingredients. Blend on low until a thick dough forms.
Fold in chocolate and walnuts until evenly distributed.
Scoop eight large mounds, about 4 ounces each, stacking them tall.
Chill the scooped dough 10 minutes to reduce spread, if kitchen is warm.
Bake 11–13 minutes until tops are set and edges browned; rest 10 minutes.