1. Preheat the oven to 400°F (200°C) and line a 12-cup muffin pan with paper liners or lightly grease each cup.

2. In a large mixing bowl whisk together the all-purpose flour, unsweetened cocoa powder, hot chocolate mix, granulated sugar, baking powder, baking soda, fine sea salt, and instant espresso powder if using until well combined.

3. In a separate medium bowl whisk the eggs, whole milk, vegetable oil, sour cream or Greek yogurt, vanilla extract, and peppermint extract until the mixture is smooth and creamy.

4. Pour the wet ingredients into the dry ingredients and gently fold together with a spatula just until you no longer see streaks of dry flour; the batter will be thick and slightly lumpy.

5. Fold in the semi-sweet chocolate chips until they are evenly dispersed throughout the batter, being careful not to overmix.

6. Divide the batter evenly among the 12 muffin cups, filling each about 3/4 full and mounding the batter slightly in the center; sprinkle the tops with coarse sugar if using.

7. Bake the muffins at 400°F (200°C) for 5 minutes, then reduce the oven temperature to 350°F (175°C) without opening the oven door and continue baking for 12–14 minutes, or until a toothpick inserted in the center comes out with a few moist crumbs attached.

8. Remove the pan from the oven and let the muffins cool in the pan for 5 minutes, then transfer them to a wire rack to cool completely before topping.

9. To make the chocolate topping, heat the heavy cream in a small saucepan or in the microwave just until steaming but not boiling, then pour it over the 3/4 cup chocolate chips or chopped chocolate in a heat-safe bowl and let sit for 2–3 minutes.

10. Stir the cream and chocolate together until smooth and glossy, creating a ganache-like drizzle, and let it thicken slightly until it coats the back of a spoon.

11. Spoon or drizzle the warm chocolate topping over the cooled muffins, letting it drip down the sides for a pretty finish.

12. Immediately sprinkle each muffin with crushed candy canes so they stick to the chocolate, then let the topping set for a few minutes before serving.