In a medium saucepan, combine heavy cream, milk, honey, and dried lavender. Warm over medium heat until steam rises and small bubbles form, about 5–7 minutes.

In a separate bowl, whisk egg yolks and sugar until pale and slightly thickened, about 2–3 minutes.

Gradually whisk about a cup of the hot cream mixture into the egg mixture to temper the eggs, then return to the saucepan over low heat.

Cook the mixture over low heat, stirring constantly until it thickens enough to coat the back of a spoon, about 8–10 minutes.

Remove from heat and strain the custard through a fine-mesh sieve into a bowl. Cool to room temperature, then refrigerate for at least 4 hours.

Pour the chilled custard into your ice cream maker and churn according to the manufacturer's instructions, about 20–25 minutes.

Transfer the ice cream to an airtight container and freeze for at least 4–6 hours until firm.