Preheat the oven to 350 degrees F. Line a 9-by-13-inch baking pan with parchment paper and spray with cooking spray.
Combine the granulated sugar, brown sugar, vanilla, salt, whole eggs and yolks in a large bowl; set aside.
Melt the butter and chocolate in a double boiler, then whisk together until fully combined. Mix in the vegetable oil. Pour the chocolate mixture into the sugar mixture and mix until fully combined. Fold in the flour and cocoa.
Pour the batter into the prepared pan and bake until a toothpick inserted in the center comes out clean, 30 to 35 minutes. Let cool completely before slicing.