Line 2 large baking pans with parchment paper. Whisk together flour, cornstarch, baking soda, and salt in a bowl. Beat butter and sugars on medium speed with an electric mixer until combined. Beat in eggs, egg yolks, and vanilla. Reduce mixer speed to low, and slowly add flour mixture until just combined. Fold in chocolate chips. Divide dough into fourths. Press into 4 6-inch disks; place 2 disks on each prepared pan. Refrigerate 4 hours or up to 2 days.  Preheat oven to 325°F. Bake cookies, rotating pans halfway through, until the edges are golden but still soft in the center, 20 to 24 minutes. Cool completely on the pans on a wire rack.  Top 3 cookies with 1 flavor of each ice cream, spreading to edges; freeze 4 hours or up to 24 hours. Stack frozen cookies on a cake plate or platter, and top with remaining cookie.  Freeze until ready to serve. Let stand at room temperature before cutting, 10 to 15 minutes. Top with chocolate sauce just before serving.