In a medium saucepan, combine heavy cream, whole milk, honey, and dried culinary lavender. Heat until it simmers for about 5 minutes, then steep for 15-20 minutes.

Strain the mixture through a fine-mesh strainer to remove the lavender, then return the strained cream to the saucepan and reheat gently.

Whisk egg yolks in a mixing bowl until light. Gradually add warm cream while whisking to temper yolks. Continue to mix in the rest of the cream.

Return the mixture to medium-low heat, stirring continuously until thickened (about 5-7 minutes). Avoid boiling.

Remove from heat, stir in vanilla extract, cover with plastic wrap pressed against the surface, and refrigerate for at least 4 hours.

Pour chilled custard into an ice cream maker and churn according to the manufacturer's instructions until soft-serve consistency (20-25 minutes).

Transfer to a lidded container and freeze for at least 2 hours before serving. Serve slightly softened for best texture.