Pour the milk and half-and-half into a medium saucepan along with the dried lavender, and bring to a gentle simmer. Once simmering, remove the pan from the heat, cover, and let the dairy and lavender infuse for 30 minutes.
While the milk is diffusing, combine the sugar, a pinch of salt, cocoa powder, and chocolate pieces in a mixing bowl.
Strain the milk and half and half in a fine mesh sieve to remove the lavender buds. Return the milk to the medium saucepan and bring the liquid to a very low simmer once again.
Turn off the stove and spoon in small amounts of the dry ingredients and stir continuously, working the dry ingredients into the milk until they are well incorporated.
Add in the vanilla extract and whisk everything together until the lavender hot chocolate is smooth.
Pour into mugs and top with whipped cream.