Place chocolate and raspberries with juice in a heatproof bowl (preferably with a spout), and set aside.
Combine milk and basil in a small saucepan and heat over medium-low heat, whisking frequently. (The faster you whisk, the foamier the milk will be.)
When the milk mixture looks like it's about to boil, remove from heat and pour through a strainer into bowl over the chocolate, catching the basil in the strainer.
Let sit about 1 minute, then whisk until completely smooth.
Pour into a blender and blend until smooth.
Pour into a mug and enjoy.