To a large saucepan, add the heavy cream and whole milk. Heat over medium, and bring the mixture just to a simmer, stirring frequently. Remove from heat.
In a large bowl, whisk together the eggs yolks until light in color. Add the sugar and honey and whisk until smooth. Temper the cream mixture into the egg mixture, by adding a little at a time while constantly whisking. Once about half of the cream mixture has been added to the egg mixture, pour the egg mixture into the saucepan, whisking constantly. Return the pan to the stove, and place over low heat. Continue cooking, stirring frequently, until the mixture has thickened to the point where it coats the back of a spoon (a temperature of 170 degrees F - use a thermometer to make your life easier). Transfer the mixture to a large bowl or container and bring to room temperature, about 20-25 minutes. Stir in the vanilla extract and lavender essential oil. Cover and place the mixture in the refrigerator to chill for at least 4 hours.
Once your ice cream base has chilled, pour it into the bowl of an ice cream maker. Process per manufacturer's instructions to desired consistency, about 25-30 minutes. Fold in frozen blueberries and transfer to an airtight container.
Serve immediately for soft serve, or cover and freeze until you are ready to serve.