Preheat your oven to 350 degrees. Prepare a muffin pan with melted butter and then dust with a little bit of flour. Pulse the sugar and lemon zest in a blender until combined. Add the eggs one at a time, then gradually pour in the olive oil and milk, pulsing until emulsified into a thin batter, about 30 seconds. Don't overblend or the cakes will be too puffy.
Whisk one cup flour, the baking powder, salt and thyme in a small bowl. Add to the blender in 2 batches until just combined. Pour the batter unto the prepared pan and bake until the cakes just start to pull away from the sides of the pan and spring back when lightly touched, about 25 minutes depending on your oven.
In the meantime, make the glaze: whisk the powdered sugar, melted butter and lemon juice until smooth, adding more lemon juice if too thick. Drizzle over the cooled cakes and garnish with a thyme sprig.
