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Heat oven to 350F. Line an 8—8 baking pan with parchment paper (or butter it generously).
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Melt the butter; add sugar, vanilla, cocoa powder, salt, red food coloring, and vinegar - stir to combine everything. In a separate bowl, whisk the eggs; add eggs to the butter mixture slowly, whisking constantly.
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Fold the flour into the mixture, being careful not to overmix. Reserve ¼ cup of batter for the top and set aside. Pour the remaining batter into the prepared baking pan.
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For the cream cheese:
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Using a stand mixer or hand mixer, beat cream cheese until soft. Add sugar, egg, and vanilla; beat until combined. Spread the cream cheese mixture over the brownie batter in baking pan.
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Dollop remaining brownie batter over the cream cheese layer. Drag a toothpick or knife through the batter to create swirls.
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Bake brownies for 25 - 30 minutes, or until the cream cheese is set. Remove to a cooling rack and allow to cool completely before cutting.