In a saucepan, combine the sugar, water and mint. Over medium-low heat, simmer the liquid for about 20 minutes, to infuse the flavors. Remove from the heat, strain the mint leaves out and cool completely. In another saucepan, over medium heat, add the cream. Bring the liquid to a gently boil. Whisk the egg yolks together. Whisk 1 cup of the hot cream into the egg mixture. Mix thoroughly. In a steady stream, slowly add the egg mixture to the hot cream mixture. Continue to cook for 4 minutes, stirring occasionally. Remove from the heat and cool completely. Strain the mixture. Whisk the mint liquid into the cream mixture. Mix thoroughly. Add the mint/cream mixture to the electric ice cream maker. Process according to manufacture's directions.