Make sure that the interior of the ice cream machine is in the freezer.
Mix the milk, cream, and honey together in a large sauce pan.
Heat the mixture on the stove until the honey is totally dissolved & incorporated...usually about 3-5 minutes. Be sure to stir constantly or the milk will scorch.
Add the vanilla extract and stir well.
Cover with plastic or a reusable wrap.
Refrigerate for an hour or put it in the freezer for 20-30 minutes to chill. Use a candy thermometer to make sure that your mixture is no higher than 32 degrees F.
Pour the chilled ice cream mixture into the machine and immediately turn on the paddle mixer.
Let the ice cream mix in the machine for 30 minutes to an hour. Stop the machine when the ice cream has reached the desired consistency. If your mixture does not freeze well, pour it back into the sauce pan and put it and the ice cream machine interior back into the freezer for a while.
Move the thickened ice cream to a storage container.