• Preheat oven to 350 degrees. Butter the bottom of or spray the bottom of 9-inch cake pan with non-stick cooking spray. You can also use parchment paper.
• In a large bowl, beat the eggs, egg yolks, brown sugar, sugar, and salt for 8-10 minutes until light and fluffy. Fold in the flour. Fold in the melted butter and vanilla.
• Pour into pan and bake for 13-16 minutes. Let cool. Cut into small squares and place in a bowl. Toss with 3/4 cup of caramel until completey coated.

Ice Cream:

• Cook the milk, cream, brown sugar, sugar, and corn syrup in a medium saucepan over medium-high heat. Bring to a boil and boil for 4 minutes. Watch carefully as it may expand and spillover.
• While it is boiling, add cornstarch and 2 Tablespoons of milk in a bowl and stir together. Add to mixture and allow to boil for one minute longer. Remove from heat. Add cream cheese and use a WHISK to incorporate it.
• Pour the mixture into a 1-gallon Ziploc freezer bag and submerge the sealed bag into an ICE BATH. Let stand for about 30 minutes, adding more ice if necessary.
• Pour the ice cream base into the ice cream maker and turn on the machine. Continue to churn until ice cream is thick and creamy.
• Pack the ice cream into a storage container, layering it with the caramel gooey butter cake. Drizzle remaining 3/4 cup of caramel throughout the ice cream (I like to set aside 1/4 cup of caramel to drizzle on right before serving). Seal with an airtight lid and freeze for at least 4 hours. Serve with extra caramel.