Preheat oven to 350°F (175°C) and prepare an 8x8-inch baking pan with parchment paper.

In a large bowl, whisk together melted unsalted butter and granulated sugar until glossy. Add large eggs, red food coloring, and vanilla extract, mixing until smooth.

Sift together all-purpose flour, salt, and Dutch process cocoa powder, then fold into the wet mixture until smooth.

In another bowl, beat cream cheese until smooth. Add granulated sugar and room temperature egg, mixing until combined.

Pour half of brownie batter into the baking pan, spread evenly, then dollop half of cream cheese mixture and swirl.

Repeat layering with remaining brownie batter and cream cheese mixture, creating swirls.

Bake for 30-40 minutes, checking doneness with a toothpick. Look for moist crumbs in the center.

Cool completely, then lift brownies out using parchment and slice into squares to serve.