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1. Preheat oven to 350°. Line a 13×9-inch baking pan with foil, letting excess extend over sides of pan; spray foil with cooking spray.
2. In a small saucepan, cook butter and chocolate over medium-low heat, stirring frequently, until melted and smooth. Remove from heat, and let cool for 10 minutes.
3. In a large bowl, beat 3 cups sugar, 5 eggs, and vanilla with a mixer at medium-high speed until thick and pale, about 6 minutes. Reduce mixer speed to medium-low. Gradually add flour, beating until combined. Stir in butter mixture. Reserve 1 cup batter in a small bowl. Spread remaining batter into prepared pan.
4. In a small bowl, beat cream cheese, remaining ¼ cup sugar, and remaining egg with a mixer at medium speed until smooth. Drop mixture by heaping tablespoonfuls onto batter in pan. Drizzle with caramel. Drop reserved 1 cup batter by heaping tablespoonfuls onto caramel. Gently swirl together cream cheese mixture, caramel, and top layer of batter with the tip of a knife.
5. Bake until center is set, 30 to 35 minutes. Let cool completely in pan on a wire rack. Using excess foil as handles, remove from pan, and cut into bars. Store in an airtight container for up to 1 week.