Preheat the oven to 350°F (176°C) and grease a 9-inch round cake pan with butter. Line the bottom of the pan with parchment paper.
In a medium bowl, whisk together the flour, baking soda and salt.
In a large bowl, cream the butter and sugars until light and fluffy, and then cream in the instant pudding mix. Beat in the egg and yolk, making sure they are fully incorporated into the batter. Mix in the vanilla extract.
On low speed, mix in half of the flour mixture at a time, until just combined. Fold in the chocolate chips. Spread the dough evenly in the prepared pan.
Bake for 22-24 minutes, or until the cookie cake is golden brown. The middle should be soft but not doughy. Let it cool completely in the pan. The cake will firm up more as it cools.Once cool, carefully flip the cake out onto a cooling rack. (It will be upside down.) Then flip the cake right-side up onto a 10-inch cake board.