Make the lime syrup:
In a small saucepan, combine lime juice and granulated sugar. Simmer over low/medium heat until the sugar dissolves and the mixture is slightly syrupy, about 3-5 minutes. Remove from heat and set aside to cool. Transfer to a small container with a tight fitting lid and place in the refrigerator until ready to use.
Make the cornstarch slurry:
In a small bowl combine the cornstarch and milk and stir until the cornstarch is completely dissolved. Set aside.
Make the ice cream base:
Prepare a large bowl with ice water. Place an open one gallon Ziploc bag inside the ice water and set aside.
In a medium saucepan combine milk, heavy cream, sugar, corn syrup, and lime zest. Bring to a boil stirring occasionally. Once mixture has boiled reduce the heat to low and add the cornstarch slurry. Whisk the mixture vigorously until the cornstarch has cooked and the mixture has slightly thickened, about 3-4 minutes. You can test by tasting the mixture. If it tastes chalky to the tongue, cook for one more minute. Remove from heat and add the mint leaves. Stir a little to moisten the mint leaves.
Transfer mixture to the prepared Ziploc bag inside the ice bath. Seal the bag and allow the ice cream base to cool completely. Once cooled, place the sealed Ziploc bag in the refrigerator for at least 5 hours or overnight to allow the flavors to meld.
Once the mixture has steeped, strain the contents into a medium bowl, pressing on the solids to extract as much of the mixture as possible. I like to submerge the solids into the base and strain 3-4 times to extract all the flavor situations. But you do you, boo.
Add the lime syrup and stir to incorporate. At this point you will notice the mixture has thickened significantly. That’s cool. It’s supposed to happen. Add the rum and stir the mixture until the rum is incorporated into the ice cream base.
Freeze according to manufacturer’s instructions. When frozen and with the help of a spatula, pour the ice cream into a quart container with a tight fitting lid. Place in the freezer and allow to solidify completely, at least 3-4 hours. Or you can just spoon soft serve mojito ice cream in your mouth. It’s cool.
Adapted from: We all Scream