In a saucepan over medium heat, whisk the heavy cream, milk, and honey until steam rises. Place the lavender in in a reusable tea bag or cheesecloth pouch, seal, and immerse it in the liquid to steep. Cover the pan, remove from the heat, and let steep for 25 minutes, then squeeze the sachet to release the flavor, and remove.
In a small bowl, whisk the egg yolks with 1/2 cup of the ice cream mixture, then gradually whisk the egg yolk mixture back into the pan. Return to the stove, and cook over low heat, stirring continuously, until the custard reaches 170ºF, 20 to 25 minutes, or until it thickens slightly and coats the back of a spoon. Remove from heat.
Use a spatula or the back of a spoon to push down the peaches in the strainer and extract any remaining juice. Pour the juice that's collected in the bowl into the lavender-steeped custard and stir to combine.
Transfer to a bowl, cover, and cool completely in the fridge.
Taste the chopped peaches for sweetness, and if the peaches are very tart, mix in honey to taste (up to 2 teaspoons). Set aside 1/3 cup of the chopped peaches to garnish the top of the ice cream.
Once the custard is fully chilled, freeze it in the ice cream maker according to the manufacturer's instructions. Once the consistency is smooth and thick, add the chopped peaches and let the churn distribute them evenly throughout. Transfer to a freezer safe container, sprinkle with the final 1/3 cup of chopped peaches, cover, and freeze for at least 4-6 hours before eating.