First, I preheated the oven to 350 °F (175 °C). Then I lined an 8×8-inch baking pan with parchment paper and greased it lightly with butter so the brownies would lift out cleanly.
In a large bowl, I whisked melted butter, sugar, cocoa, vanilla, food coloring, and salt until smooth, then stirred in vinegar. Next I folded in the eggs, one by one, and gently stirred in the flour until just combined (don’t overmix).
I beat the cream cheese, sugar, vanilla, and egg yolk until creamy and smooth. Then I poured most of the brownie batter into the pan, spread it flat, and dolloped the cheesecake mixture on top. I topped that with the remaining brownie batter in small spoonfuls.
Using a toothpick or skewer, I lightly swirled the cheesecake and brownie layers for a marbled effect (don’t overdo it). Then I baked for 30 minutes until set around the edges (center may still jiggle slightly). After baking, I let them cool completely before lifting out and slicing.