Red Velvet Bread Pudding

INGREDIENTS

• Pinch salt
• 3 cups half-and-half
• 2 cups sugar
• 1 cup buttermilk
• 2 eggs
• 2 tablespoons cocoa powder
• 1 tablespoon vinegar
• 8 ounces cream cheese, at room temperature
• 1 teaspoon vanilla extract
• 2 ounces red food coloring
• 1/2 pound (2 sticks) butter, at room temperature
• 3/4 cup confectioners' sugar
• 2 1/2 cups cake flour
• 1 teaspoon salt
• 1/2 teaspoon baking soda
• Vanilla ice cream, for serving
• 1 large egg yolk
• 3 large eggs