In a saucepan, combine the bourbon, simple syrup, and mint. Over medium-low heat, simmer the liquid for about 10 minutes, to infuse the flavors. Remove from the heat and cool completely.

In another sauce pan, add the cream. Bring the liquid to a gentle 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 bourbon mixture. Whisk the bourbon liquid into the cream mixture. Mix thoroughly. Add the bourbon/cream mixture to the electric ice cream mixture. Process according to manufacturer's directions. To assemble, place a large scoop of the ice cream in the center of each serving dish. Garnish each with fresh mint.