Blend cream cheese (if using): In a blender, mix softened cream cheese with 1 cup of milk until smooth and lump-free.
Heat mixture: In a heavy saucepan, combine the cream cheese mixture (or plain milk if skipping), remaining milk, heavy cream, sugar, cocoa powder, white chocolate, vanilla, and salt.
Whisk gently: Place over medium heat, whisking constantly, until the chocolate melts and the mixture is smooth. Do not let it boil.
Add color: Stir in red food coloring drop by drop until you reach a deep, rich red velvet shade.
Prepare topping (optional): Beat softened cream cheese, sugar, and vanilla until smooth. Gradually add heavy cream and whip until fluffy peaks form.
Serve: Pour hot chocolate into mugs. Top with whipped cream, cocoa powder, or chocolate shavings. Serve immediately.
