(1) Warm the milk in a saucepan or hot chocolate pot over medium heat, just until steaming. Whisk in the chocolate until completely melted.
(2) Bring the mixture to a simmer, being careful not to let it boil over. Let simmer, whisking constantly, for 3-5 minutes, until it thickens slightly.
(3) Remove from heat and add the brown sugar and salt. Whisk rapidly to combine and froth, or use the pot's built-in frother.
(4) Divide the Green Chartreuse evenly between four mugs (2 oz per mug), and top with the hot chocolate.