4 ounces coarsely chopped bittersweet or semisweet chocolate
2 teaspoons corn syrup
1/2 teaspoon vanilla extract
To make the chocolate chip cookie layers, melt butter in a small saucepan over medium heat; continue to cook the butter, whisking frequently, until it starts to brown and foam, about 4-5 minutes. Set aside.
In a medium sized mixing bowl, sift together flour, baking soda and salt.
In a large mixing bowl, using a mixer on medium speed, beat browned butter, brown sugar and granulated sugar until well combined and grainy, about 1 minute. Beat in eggs and vanilla until well combined. Reduce mixer speed to low and gradually beat in flour mixture until just combined; stir in chocolate with a wooden spoon until combined. Chill dough in the refrigerator, lightly covered, for 1 hour. (You could speed up this process by placing the dough in the freezer for about 45 minutes.)
Preheat oven to 350 degrees F. Butter and flour 2 (9-inch) cake pans.
To make the chocolate cake layers, in a medium bowl, sift together flour, cocoa powder, baking soda and salt.
In a large mixing bowl, using a mixer on medium speed, beat together oil, butter and granulated sugar until well combined and creamy, about 1-2 minutes. Beat in egg, vanilla and yogurt until combined. Reduce mixer speed to low and gradually beat in flour mixture until combined, about 1-2 minutes.
Divide batter into cake pans. Bake 15-20 minutes or until a toothpick inserted into cakes comes out with moist crumbs attached. Cool pans on wire racks for 10 minutes; run a knife around outside edges and invert onto wire racks to cool completely.
Increase oven temperature to 375 degrees F. Butter the cake pans again, and line with parchment or waxed paper circles; butter paper.
Divide cookie dough and pat evenly into pans. Bake for 15-20 minutes or until golden brown. Cool completely in pan before running a knife around outer edges and lifting out paper-lined cookies; remove paper.
Spread the ice cream evenly between cookie and cake layers; freeze for 10 minutes before covering with ganache. Meanwhile, to make the ganache, bring cream to a simmer in a small saucepan over medium heat. Remove pan from heat and stir in chocolate until melted and smooth. Cool to a good consistency before pouring over ice cream cake.