Pour the milk into a saucepan and warm over medium heat until tiny bubbles form around the edges, about 3-5 minutes. Keep an eye on it to avoid boiling.
Add the dark chocolate chips to the warm milk and whisk gently until the chocolate melts completely and the mixture becomes smooth and glossy. This should take about 2-3 minutes.
Remove the saucepan from heat and stir in the peppermint extract, adjusting the amount to your preference for a bright, fresh mint flavor.
Pour the hot chocolate into mugs, filling them to your desired level. The drink should be rich and velvety with a warm aroma of chocolate and peppermint.
Top each mug with a generous dollop of whipped cream, creating a fluffy, white crown over the chocolate.
Sprinkle crushed peppermint candies over the whipped cream for a festive, crunchy garnish that adds both flavor and visual appeal.
Serve immediately while steaming hot, and enjoy the delightful contrast of creamy chocolate and cool peppermint with every sip.