Chocolate – How to make chocolate milk

I have tried making hot cocoa with melted chocolate. Here is how I did it:

Heat up some milk in a mug until it is hot(ceramic tends to do better in microwaves than glass does because it doesn't conduct heat as well as glass does.)

Put half milk chocolate and half dark chocolate(I was trying to go for that bittersweet and semisweet chocolate by using milk chocolate and dark chocolate) in a small thin glass container and melt it completely(not to the point of separation though)

Put a little bit of the hot milk in the chocolate to temper it(same way you temper eggs).

Stir the chocolate into the milk. Now this chocolate was hershey's brand and I used 4 pieces of the milk chocolate and 4 pieces of the dark chocolate.

Keep stirring until it is the same color as chocolate milk or darker.

Now doing it this way I thought "Milk has fat and water and chocolate has water soluble components and fat soluble components so it should be all good with no separation.

However it did separate and there was a little bit(about an 1/8 of an inch of cocoa butter at the top.

However you can't homogenize chocolate like you can homogenize milk.

Now my thought on why it didn't work is because I used 2% reduced fat milk(which means fat is reduced by 2 percent not to 2%) and so there was too little fat.

Even though it was only reduced by a little in terms of fat content, that little bit it was reduced by might be important to prevent separation. However I didn't want to go with organic milk because I know that organic milk separates into water and cream.

So if I want to make hot cocoa using chocolate or make chocolate milk should I go with whole milk and melt the chocolate over the milk in a double boiler or what?