Combine milk, cream, and half of the sugar in a medium saucepan and heat on medium-low flame. Split the vanilla bean in half down the middle, chop into large pieces, and add to saucepan. Stir mixture constantly while cooking. When mixture begins to boil, stir in vanilla sugar, honey, corn syrup, lavender, and extract.
Lower heat and simmer for 15-20 minutes, constantly stirring. Remove from heat, strain, and set aside to cool. Remove one cup of the cream mixture and set aside. In a small bowl, combine egg, egg yolks, and remaining sugar in a bowl. Using a hand mixer set on medium, beat the mixture until it is thick and smooth (about 2-3 minutes).
Take the cooled cup of cream mixture and slowly mix it into the egg mixture, stirring constantly. When combined, return the new mixture into the rest of the cooled cream mixture. Return saucepan to a low flame and cook, stirring constantly until the thickness can cover the back of a spoon. Strain, then transfer mixture to a bowl and set aside to cool for 10 minutes, cover with plastic wrap, and set in refrigerator to chill for 3 hours.
Pour chilled custard mixture into ice cream maker and turn on per machine's instructions. When thickened, the ice cream will have a soft, creamy texture. Transfer ice cream to air tight containers and set in freezer. |