Pour milk, sweetener and vanilla extract into a medium size saucepan then warm it up.
Separate egg yolks from the whites as only the yolks will be used.
Take about a cup of the warmed up milk and gradually stir it in with the yolks. It’s important to raise the temperature of the yolks before pouring it into the hot milk as this will prevent clogging of the egg.
Pour back the warmed up egg yolks and milk into the saucepan with the hot milk-vanilla-agave mixture while stirring mildly on low to medium heat. Keep stirring on low to medium heat frequently until it starts bubbling.
Dissolve cocoa powder with 4-6 tbsp warm milk in a small cup then mix it in.
Put chocolate chunks into the saucepan as well.
Stir frequently until chocolate melts completely and incorporates well with the other ingredients. Take it off the heat and let it cool down.
Whip cream until hard peaks form.
Mix chocolate base and whipped cream carefully so the ice cream will have a light fluffy texture.
Pour it into the container and put it in the freezer for 4-6 hours. Stir it every 30 to 60 minutes to avoid the crystallization of the water in the cream.