Heat 3 1/2 cups of milk over medium heat until the milk begins to bubble around the edges.
Meanwhile, whisk together the remaining 1/2 cup milk and cornstarch until dissolved. Set aside.
Chop or grate the chocolate. The finer the pieces, the faster it will melt in the hot milk.
When the milk begins to bubble around the edges, add the chocolate, honey, vanilla, and sea salt.
Whisk in the milk and cornstarch mixture.
Let the hot chocolate come to a bubble, stirring occasionally. It should take about 5 minutes. The mixture will thicken, let cool slightly, and ladle into mugs.