Prepare the Cakes: Combine chopped semisweet chocolate and heavy cream in a small microwave-safe bowl. Microwave on high 30 seconds. Let stand 1 minute; whisk until melted and smooth. Place plastic wrap directly on chocolate mixture (to prevent a skin from forming); chill until firm, about 2 hours. Chocolate mixture can be prepared 1 day in advance; store, covered, in the refrigerator.

Preheat oven to 400°F. Grease 4 (8-ounce) ramekins with butter; dust with unsweetened cocoa, and tap out excess. Whisk together flour, cocoa, baking soda, and salt in a medium bowl. Whisk together melted butter, granulated sugar, buttermilk, food coloring, vanilla, vinegar, and egg yolk in a separate bowl. Add butter mixture to flour mixture, and whisk just until blended. Divide batter evenly among prepared ramekins.

Using a small (1 1/4- or 1 1/2-inch) cookie scoop, portion chilled chocolate mixture into 4 balls. Place 1 chocolate ball in center of batter in each ramekin, pressing lightly. (Chocolate will sink into batter as it bakes.) Place ramekins on a baking sheet. Bake in preheated oven until center springs back when lightly pressed, about 18 minutes.

Meanwhile, prepare the Cream Cheese Whipped Cream: Stir together cream cheese, powdered sugar, and vanilla in a medium bowl until smooth. Add heavy cream; beat with an electric mixer on medium-high speed until soft peaks form, 30 seconds to 1 minute, scraping down sides of bowl as needed.

Remove cakes from oven. Immediately run an offset spatula or thin knife around outer edge of cakes to loosen; invert each red velvet cake onto a serving plate. Dust cakes evenly with powdered sugar. Top cakes with Cream Cheese Whipped Cream, and serve immediately.