Preheat oven to 300°.
Sift both flours, cornstarch, baking powder, and salt together into a medium bowl. Set aside.
Using an electric mixer, beat together butter and sugar at medium speed until smooth. Scrape sides as needed. Mix in vanilla until blended. Decrease mixer speed to low and add flour mixture. Mix just until combined and a smooth dough has formed.
Use about 1/2 tablespoon of dough for each cookie. Roll each into a ball and place about 2 inches apart on lined baking sheets. Flatten each with a fork to about 1 & 1/4 inches in diameter.
Bake sheets one at a time until the bottoms of the cookies begin to brown, about 25-30 minutes. The tops should not change color. Cool on pan for about 10 minutes, then transfer to wire racks to cool completely.
Stir together butter, sugar, and vanilla until smooth. Stir in chocolate chips.
Turn half of the cookies over and spread about a teaspoonful of filling on each. Place the remaining cookies on top of the filling. Press gently.
Makes 16 sandwich cookies (32 individual cookies).