Prep the mixture: Pour 2 cups heavy cream, 1 cup whole milk, 3/4 cup granulated sugar, 1 tablespoon vanilla extract, 1/2 teaspoon peppermint extract, and 1/4 teaspoon salt into a large mixing bowl. Whisk together vigorously for 2 minutes until the sugar completely dissolves and you can no longer feel any grittiness at the bottom of the bowl. Checkpoint: When you run a spoon along the bottom, it should feel smooth.
Melt the chocolate: Place 1 cup semi-sweet chocolate chips and 2 tablespoons coconut oil in a small heatproof bowl. Set the bowl over a pot of gently simmering water (the bowl should not touch the water). Stir occasionally with a rubber spatula for 3–5 minutes until the chocolate is completely smooth and melted. Do not overheat—if the chocolate steams, it may seize. Checkpoint: The chocolate should be pourable like warm syrup with no visible lumps.
Chill the base (if using an ice cream maker with a freezer bowl): Refrigerate your mint mixture for at least 30 minutes if it feels warm to the touch. Meanwhile, ensure your ice cream maker's freezer bowl has been frozen for at least 24 hours according to the manufacturer's instructions. Checkpoint: The base should feel very cold to the touch.
Churn the ice cream: Pour the chilled mint mixture into the ice cream maker. Turn it on and let it churn for 20–25 minutes, following your machine's instructions. The mixture will gradually thicken and become pale, and you should see ice cream forming along the sides of the churn.
Add chocolate in the final moments: When the ice cream is almost done (about 20 minutes in), slowly pour the melted chocolate into the machine while it continues to churn. Pour in thin streams so the chocolate breaks into small chips as it hits the cold ice cream. Do not pour it all at once or you'll create one large chocolate mass. Checkpoint: You should see small dark chocolate chunks distributed throughout the pale green ice cream. The consistency should resemble soft-serve yogurt.
Freeze to firm consistency (optional): If you prefer scoopable ice cream rather than soft-serve, transfer the churned ice cream to a freezer-safe airtight container and freeze for 2–3 hours until firm. If freezing for longer than 4 hours, remove from freezer 5–10 minutes before scooping to soften slightly.
Serve: Scoop into chilled bowls or cones. Mint chocolate chip ice cream is best eaten within 1–2 weeks of freezing to preserve texture and flavor.