Bring water in the bottom of a double boiler to boil.
Pour half and half and mint leaves into the top of double boiler and put over boiling water.
Crush or chop the unsweetened Baker's chocolate and add to milk and mint, stirring to melt chocolate.
Add cocoa powder to hot milk mixture. Stir until milk is scalded, all chocolate is melted.
Remove from heat.
Whisk together egg yolks and sugar/Splenda (can use half sugar, half baking Splenda).
Strain chocolate, mint mixture and press through a fine sieve.
Pour a very small amount of chocolate mixture into the egg yolks and whisk vigorously. You do not want the yolks to cook. Continue until you've whisked in about 1/3 of the chocolate.
Add tempered yolks, sugar, and chocolate mixture to the remaining chocolate, half and half mixture. Add salt.
Stir over low heat until the mixture thickens, and when you lift a wooden spoon out of the mixture it coats the back of the spoon.
Remove from heat and continue stirring. Put into fridge to cool down. Stir every 30 min or so to ensure it cools evenly.
Let cool 4-8 hours or overnight.
Pour into your prepared ice cream maker, add rum, and mix per directions. The rum is to lower the freezing temperature, so only add at the end or the alcohol cooks off.
For soft serve, serve immediately or for a harder ice cream, freeze for 2 hours before serving. If you don't eat it all that evening, remove from freezer and let sit for 30 minutes to make it easier to scoop as all homemade ice cream freezes hard.