Combine all ingredients in a saucepot over low heat. Stir with a spatula to dissolve the sugar and chocolate.
Bring to a simmer for 5-10 minutes, stirring with the spatula and being sure to scrape the bottom of the pot. Simmer for up to 10 minutes for a thicker, richer final result.
Fish out the ginger pieces and serve hot.
Notes
I tested this recipe with 55% dark chocolate, but feel free to customize it to your taste. Use a higher cacao dark chocolate for a more intense flavor or opt for milk chocolate if you prefer a sweeter, creamier cup.