Special equipment: 2 nonstick cupcake tins; cupcake liners; a pastry bag or resealable plastic bag fitted with a large star tip
Preheat the oven to 350 degrees F.
For the lavender sugar: Put the lavender in a food processor or blender on high speed; process until finely ground. Remove 1 tablespoon of the lavender and set aside. Add the palm sugar to the remaining lavender and process to a very fine powder. Store in an airtight container until ready to use.
For the cupcakes: In a stand mixer fitted with the paddle attachment, cream together the butter, honey and 6 tablespoons of the lavender sugar. Add in the eggs and lemon oil and mix until smooth.
In a bowl whisk together the flour, baking soda, sea salt and the 1 tablespoon reserved ground lavender. With the mixer on low speed, slowly incorporate half of the flour mixture. Next mix in the lemon juice. (The mixture may look curdled but it is not.) Mix in the remaining flour mixture and then the milk and lemon zest. Continue mixing until the batter is totally smooth.
Double line 1 1/2 standard, nonstick cupcake tins with liners. Fill the liners with a heaping 1/4 cup of the batter. Bake until a toothpick inserted into the center of the cupcakes comes out clean, 16 to 18 minutes. Remove from the oven and let cool until easy to handle. While still slightly warm, dip the tops of the cupcakes in another 6 tablespoons lavender sugar. Place on baking sheet and let cool completely.
For the lemon frosting: Melt the white chocolate over a double-boiler. Allow to cool slightly but don't let the chocolate set.
In the bowl of a stand mixer fitted with the whip attachment, whip together the cream cheese, butter, lemon oil and sea salt. Slowly add in the melted white chocolate and mix until smooth. Spoon the frosting into a pastry bag fitted with a large star tip and refrigerate until set.
Pipe the frosting onto the cupcakes and garnish with the edible flowers.