Preheat oven to 410°F (210°C). Line baking sheets with parchment paper.
In a large bowl, cream cold cubed butter, brown sugar, and granulated sugar for about 4 minutes, until creamy but still thick.
Add eggs one at a time, mixing well after each addition. Stir in vanilla extract and vanilla bean paste.
Add cake flour, all-purpose flour, cornstarch, baking soda, and salt. Mix just until combined.
Fold in chocolate chips and walnuts gently.
Scoop dough into large 2.66 oz (75 g) balls. You should get about 15 cookies.
Place 5 cookies per baking sheet, spacing well apart.
Bake for 11 minutes, until the tops are lightly golden and the centers look slightly underbaked.
Let cookies rest on the tray for 10 minutes before serving.
