Preheat oven to 350°F. Line an 8-inch square metal baking pan with foil, draping foil over edges. Mist with cooking spray.
In a small saucepan, melt butter over medium heat. Remove pan from heat and stir in chocolate until melted and smooth. Let cool.
In a large bowl, whisk together brown sugar, 3/4 cup sugar, eggs, 1 1/2 tsp. vanilla and 1/2 tsp. salt until smooth and pale, about 30 seconds. Stir in cooled chocolate mixture and buttermilk. Stir in flour until just combined. Stir in quartered Oreos, then pour batter into baking pan.
In a small bowl, stir cream cheese, 2 Tbsp. sugar, 1/4 tsp. vanilla and 1/4 tsp. salt until smooth. Scrape into a small ziplock bag. Snip off 1 corner of bag with scissors, then squeeze cream cheese mixture in a swirled pattern over the batter in pan.
Bake until a toothpick inserted into brownies comes out clean, 55 to 60 minutes. Transfer pan to a rack and let cool completely. Lift brownies out of pan, remove foil and cut into 12 pieces. Wrap brownies in plastic wrap and store at room temperature for up to 5 days.