In a medium saucepan, combine 2 cups of whole milk, 1 cup of heavy cream, 1 cup of sugar, and ½ cup of cocoa powder. Place over medium heat, whisking continuously until the mixture is warmed and the sugar fully dissolves but avoid boiling.

Whisk 5 egg yolks in a separate bowl until they lighten in color. Gradually add about ½ cup of the warm milk mixture to the yolks, whisking continuously to prevent cooking the eggs.

Continue cooking the custard over low heat, stirring constantly with a wooden spoon for 8 to 10 minutes, until it thickens enough to coat the back of the spoon.

Remove the custard from heat and whisk in 8 ounces of cream cheese, 2 teaspoons of vanilla extract, 1 tablespoon of red food coloring, and 1 tablespoon of fresh lemon juice (if using). Mix until completely smooth and creamy.

Once cooled, transfer the custard to an airtight container and refrigerate for at least 4 hours or overnight.

After chilling, pour the mixture into your ice cream maker according to the manufacturer's instructions. Churn for about 20-25 minutes, or until it thickens to a soft-serve consistency.

Transfer the churned ice cream into a lidded container, smooth the top with a spatula, and freeze for at least 4 hours before serving.