To make the ice cream, in a saucepan over medium heat, combine the mint, cream, milk and sugar and heat, stirring occasionally, until small bubbles appear along the edges of the pan. Remove from the heat and let stand for 1 hour.

Meanwhile, make the truffles: Place the chocolate, butter and cream in the top pan of a double boiler or in a heatproof bowl and set over a pan of gently simmering water; do not allow the bowl to touch the water. Stir often until the chocolate melts, then immediately remove the pan from the heat and stir in the crème de menthe. Pour the mixture into an 8-inch cake pan and place in the freezer until cold, about 1 hour.

Shape the cold chocolate mixture into truffles: Dip a 1/2-tsp. measuring spoon or a tiny melon baller into boiling water, quickly scoop out a truffle and place on a baking sheet. Repeat until all the truffles are formed, arranging them in a single layer and making sure that they do not touch one another. Place in the freezer until thoroughly chilled, about 1 hour.

While the truffles are chilling, finish making the ice cream: Reheat the cream mixture until small bubbles appear along the edges of the pan. Remove from the heat. In a large bowl, whisk the egg yolks until blended. Slowly pour the hot cream mixture into the egg yolks, whisking constantly. Return the mixture to the saucepan and place over medium heat. Cook, stirring constantly, until the mixture coats the back of a spoon. Strain through a fine-mesh sieve into a clean bowl. Stir in the crème de menthe and refrigerate until cold.

Transfer the mixture to an ice cream maker and process according to the manufacturer's instructions. Fold in the chilled truffles during the final 1 minute of freezing. Serve immediately or pack into a container and freeze for up to 10 days.