Toss the sliced strawberries with the vanilla and a few teaspoons of the sugar while you prepare the custard.
Combine the sugar, mint leaves, heavy cream, and whole milk in a saucepan over medium heat. Stir constantly until it is hot and the sugar is dissolved. Remove from heat.
Whisk the egg yolks in a separate bowl. Add a little bit of the hot milk mixture into the eggs and stir. Gradually add small amounts of hot milk to the egg yolks until you have about equal amounts of hot milk and eggs and milk. You don't want to pour the eggs directly into the hot milk or your eggs will scramble. Not pretty.
Pour the egg/milk mixture back into the saucepan. Gradually heat the milk mixture over medium to medium high heat, stirring constantly, and being careful to not let the mixture come to a boil. You will notice the custard will gradually thicken.
When the custard is thick enough that you can draw a line on the back of your spoon - your custard has thickened enough. Remove from heat.
Let your custard cool down before you use it in your ice cream machine or ice cream ball. Ideally, I like to keep it in the refrigerator for a few hours before I pour it into my ice cream maker.
Don't add the strawberries into the custard until you are ready to pour everything into your ice cream maker. Follow the directions on your favorite ice cream machine and watch it turn into beautiful strawberry mint ice cream! Enjoy!