In a small, heavy saucepan, combine cream, milk, sugar, and lavender. Place over medium-high heat and, with a wooden spoon, bruise and crush the herbs against the bottom and sides of pan while bringing mixture just to a boil. Remove from heat. Set aside for 15 minutes to allow the lavender flavor to infuse the cream mixture. Strain through a fine sieve into a bowl, pressing on solids. Discard the lavender flowers.
Whisk the eggs in a small bowl. Gradually whisk a ladleful of the cream mixture into the eggs, then pour the eggs back into the cream mixture, whisking.
Cook over medium heat, stirring gently, for about 8 to 10 minutes or until the mixture thickens enough to coat the back of a wooden spoon. Do not boil. Transfer this mixture to a bowl, cover, and refrigerate until cold.
Pour into ice cream maker and freeze according to manufacturer's directions.
Optional: The leaves won't give up much of their green color, so you can add 1 or 2 drops of red or green food coloring. Also, you can add a handful of crushed peppermint candies just 1 second, not 2, before turning off the ice cream maker.