Preheat your oven to 400°F (200°C) and line a baking sheet with parchment paper for easy cleanup.
In a small bowl, gently whisk together all the spices listed for the "Chai Spice Blend" until they're perfectly combined. This is your secret to cozy flavor!
In a large mixing bowl, whisk together the all-purpose flour, cake flour, cornstarch, baking soda, baking powder, salt, and one heaping tablespoon of your freshly prepared chai spice blend. Set this dry mixture aside.
In a stand mixer (or using a hand mixer, allow butter to soften slightly first), cream the cold, cubed butter with both the white and brown sugars until the mixture is light and fluffy, usually about 1-2 minutes.
Beat in the eggs, extra egg yolks, and vanilla extract until everything is smoothly blended. Don't forget to scrape down the sides of the bowl to ensure all ingredients are well incorporated.
Gradually add the dry flour mixture to the wet ingredients, about 1/4 cup at a time, mixing until just combined. Be careful not to overmix the dough to keep your cookies tender.
Roll the dough into approximately 6-7 large cookie balls for impressive, giant cookies, or make them smaller if you prefer, which will yield about 20-22 regular-sized cookies.
In a separate small bowl, mix 1 tablespoon of sugar with the remaining chai spice blend (this should be roughly 1 tablespoon of the blend). Roll each cookie dough ball generously in this aromatic sugar-spice mixture.
Place the spiced cookie balls on your prepared baking sheet, ensuring there's some space between them. Bake for about 10-11 minutes for large cookies, or 8-10 minutes for smaller ones, until their edges are lightly golden. Let them cool completely on the baking sheet before glazing.
While the cookies cool, prepare your glaze. In a medium bowl, whisk together the confectioners' sugar, milk, and vanilla bean paste until it's smooth and thick. Add a tiny bit more milk if needed to achieve your desired consistency.
Once the cookies are completely cool, spoon the delicious vanilla bean glaze over each cookie or dunk them for full coverage. Allow the glaze to set for a bit, then get ready to savor these delightful, homemade chai cookies!