Peel a 1-inch piece of ginger. Grate on a Microplane until you have ½ teaspoon grated ginger. Grate 2 garlic cloves. Place the ginger and garlic in a small saucepan.
Add 1 cup ketchup, ⅓ cup packed dark brown sugar, ¼ cup tamarind concentrate or ½ cup tamarind pulp reduction, 1 teaspoon Worcestershire sauce, 1 teaspoon Dijon mustard, ½ teaspoon hot sauce if desired, and ½ teaspoon kosher salt. Season with a few grinds of black pepper. Stir to combine and bring to a gentle simmer over low heat.
Add 1 whole, untrimmed habanero pepper. Simmer, stirring occasionally, until reduced slightly and thick enough to coat the back of a spoon, 10 to 20 minutes. (Tamarind concentrate will be quicker.)
Add ¼ cup apple cider vinegar for a rich, sweet sauce, or ½ cup for a more tangy sauce. Stir to combine and simmer for 5 minutes more for the flavors to meld. Taste and season with more salt and pepper as needed.
Transfer to a serving bowl or storage container and let cool to room temperature. Remove and discard the habanero before using or refrigerating.
