Preheat oven to 350°F. Spray a 10-inch cast iron skillet with nonstick cooking spray.
In a medium bowl, whisk the flour, cornstarch, baking soda, and salt together until combined; set aside.
In the bowl of a stand mixer fitted with the paddle attachment, beat the butter and both sugars together on high until fluffy, about 2 minutes. Add the eggs, one at a time, followed by the vanilla and almond extract, scraping the sides of the bowl if necessary.
Add the flour mixture, mixing until just combined. Stir in the animal cookies until evenly incorporated. Press half of the dough into the skillet. Place the frozen frosting dollops evenly over the dough. Cover with the remaining dough by pressing portions of dough between your palms, then piecing them together on top of the frosting dollops. Make sure all of the frosting is covered.
Bake for 28-32 minutes, or until the edges are lightly golden and the center looks glossy and not quite done. Pizookie will continue to bake as it cools. Immediately press Circus Animal Cookies into the top of the Pizookie. Wait at least 45 minutes before slicing into the cookie. Serve with ice cream, if desired.