Mix the heavy cream and milk in a saucepan with a tight fitting lid.
Bring to just a simmer, where it's warm to the touch but not boiling. Remove from the heat and add the loose tea and lavender buds and stir well to combine.
Cover the pan with the lid and let steep for 5-10 minutes.
Strain the tea leaves and lavender out, using a mesh strainer.
In a separate (large) bowl, mix the egg yolks and sugar together.
A spoonful at a time, add the warm cream mixture, keeping the eggs constantly in motion. Once all of the cream and all of the eggs have been mixed, strain the combined mixture over the mesh strainer back into the saucepan.
Cook the combination mixture over medium heat, stirring almost constantly, until the mixture is thick enough to coat the back of a spoon.
Add the purple food coloring at this step, use your creativity and judgement to decide how purple you want yours to be.
Pour the mixture into a bowl and wrap tightly with plastic wrap. Refrigerate until chilled, or overnight.
Pour mixture into ice cream maker and follow the manufacturer's instructions. Once the ice cream starts thickening up considerable, add in the dark chocolate shavings and let those mix in until the ice cream is ready.
Decant to freezer-safe storage containers and let ripen overnight in the freezer before eating.