Heat the oven to 180 degrees Celsius with the rack in the middle of the oven. Brush a 12-cup mini Bundt pan with melted butter and dust it with flour, shaking out any excess flour.

In a  bowl, whisk together flour, baking powder, salt and lavender and set aside. In a food processor or blender, pulse the sugar and lemon zest together until combined. Pulse the eggs in one at a time, then gradually pour in the olive oil, milk and honey, pulsing until the batter has emulsified into a thin batter, about 30 seconds (be careful not to over-blend a this point or else the cakes will be too puffy).

Add the reserved flour mixture to the food processor or blender in two batches, pulsing until just combined both times. Pour the batter into the prepared pan, filling each cup only 3/4 of the way full. Bake for 20 to 25 minutes until the cakes start pulling away from the sides of the pan and spring back when touched. Cool for 10 minutes in the pan before inverting them onto a rack to cool completely.