Make the peppermint syrup: Combine the granulated sugar and water in a small saucepan over medium heat, stirring until the sugar dissolves. Simmer gently for 1–2 minutes, then remove from heat and stir in the peppermint extract. Cool 5–10 minutes.
Pull a double shot of espresso (2 ounces) into a 10–12 ounce mug.
Steam the whole milk to 150–160°F until silky with a thin layer of microfoam, 30–60 seconds; or heat on the stove until steaming and whisk vigorously to foam.
Stir 1–2 tablespoons of the peppermint syrup into the espresso to taste.
Pour in the steamed milk, holding back the foam, then spoon a little foam on top. Garnish with whipped cream and a sprinkle of crushed peppermint candy (for serving). Serve immediately. Store leftover syrup covered in the refrigerator for up to 2 weeks.