Place the marshmallows, 1 cup of the crushed candy, and hot water in a large microwave-safe glass bowl. Heat for 2 minutes.
Carefully remove the bowl from the microwave and stir. Return to the microwave and heat another minute, then stir until the mixture is smooth. Cool, then refrigerate the peppermint syrup until it is completely chilled, about 2 hours.
Using a chilled bowl and beaters, beat the heavy cream until still peaks form. Gently mix in the half and half. Stir in the chilled peppermint syrup.
Turn the ice cream maker on, then pour the mixture into the freezer bowl. Churn until the ice cream is thickened, about 40 minutes. Add the remaining 3/4 cup of crushed peppermint candies through the ingredient spout and churn another 5 minutes.
Serve immediately for soft serve ice cream, or ripen in the freezer for an additional 2 hours for scoopable ice cream.
This mint ice cream recipe has a high sugar content, so it takes a little longer to freeze and melts a little quicker once removed from the freezer.The texture will be soft right out of the machine. If you prefer a firmer, scoopable dessert, smooth the peppermint ice cream into a metal loaf pan and freeze for an additional 2 hours.