Preheat your oven to 425°F (220°C) and grease two ramekins with butter.
Melt the butter and white chocolate together in a microwave-safe bowl, stirring every 30 seconds until smooth.
In a separate bowl, whisk the egg, egg yolk, and sugar until pale and thick.
Stir the melted chocolate mixture and vanilla extract into the egg mixture until well combined.
Fold in the flour, cocoa powder, and red food coloring until the batter is smooth.
Divide the batter evenly between the prepared ramekins.
Place the ramekins on a baking sheet and bake for 12 minutes, just until the edges are set but the center is still soft.
Let the cakes cool for 1 minute, then carefully invert each onto a plate.
Serve immediately, optionally with a scoop of ice cream or whipped cream.