Combine the milk, sugar, heavy cream, and salt in a saucepan and gently warm until bathwater warm. Squeeze mint leaves in your hands to help release the oils a bit and add to warm milk mixture. Remove pan from heat, cover, and set aside for 30 minutes-2 hours (depending on how minty you'd like the ice cream to be.)
Strain out and discard the mint leaves (we'll often give the mint leaves another squeeze over the milk mixture to extract as much of the delicious minty-ness you can out of them).
Gently re-warm the minted milk/cream mixture, and in a separate medium bowl whisk together the egg yolks. Slowly pour the mint mixture into the egg yolks, whisking constantly. Pour this mixture back into the saucepan and return to the heat.
Heat over medium heat, stirring constantly, until the mixture thickens and coats the back of the spoon. Pour the mixture through a fine mesh strainer into a medium bowl. Place the bowl in an ice bath and stir occasionally to cool.
Cover with plastic wrap and chill the mixture in the refrigerator until fully chilled.