Combine heavy cream, milk, and mint leaves in a heavy-bottomed saucepan. Heat over medium heat until small bubbles form around the edges. Remove from heat and let steep for 30 minutes. Strain out mint leaves, pressing them gently to extract maximum flavor.

Whisk egg yolks and sugar in a large bowl until pale and ribbony, about 3 minutes of vigorous whisking. Slowly pour the warm mint-infused cream into the egg mixture, whisking constantly to prevent scrambling.

Return mixture to saucepan and cook over medium-low heat, stirring constantly with a wooden spoon. Cook until custard coats the back of the spoon and registers 170°F on a thermometer.

Remove from heat and stir in bourbon, salt, and a few drops of green food coloring if desired. Strain the mixture through a fine-mesh sieve to ensure smoothness.

Cover custard with plastic wrap pressed directly onto surface to prevent skin formation. Refrigerate at least 4 hours or overnight. Churn in ice cream maker according to manufacturer's directions, usually 20-25 minutes. Add chocolate chips in final 2 minutes if using.