Position a rack in the middle of the oven; preheat to 350 degrees. Prepare the cakes: Brush a 6- or 12-cup mini Bundt or muffin pan with the melted butter. Lightly dust with flour and shake out the excess.
Pulse the granulated 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 1 cup flour, the baking powder, salt and 1 teaspoon thyme in a small bowl. Add to the blender in 2 batches, pulsing lightly until just combined; stop to scrape down the sides of the blender as needed. Pour the batter into the prepared pan. Bake until the cakes just begin to pull away from the sides of the pan and spring back when lightly touched, 28 to 30 minutes for a 6-cup Bundt pan and 22 to 25 minutes for a 12-cup Bundt or muffin pan. Cool in the pan for 10 minutes, then loosen the sides with a small knife and invert the cakes onto a rack.
Meanwhile, prepare the glaze: Whisk the confectioners' sugar, lemon juice and butter until smooth, adding more lemon juice if the mixture is too thick. Drizzle over the warm cakes and garnish with thyme sprigs.
Photograph by Kana Okada
Courtesy of Food Network Magazine
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