Preheat the oven to 350 degrees F. Coat a 9-by-5-inch loaf pan with cooking spray and line the bottom with parchment paper. Coat the parchment with cooking spray.
Thinly slice 2 lemons and remove the seeds; set aside for topping. Grate the zest of 2 lemons. Squeeze enough of the lemons to measure 1/2 cup juice.
Whisk the flour, baking powder and salt in a medium bowl. Beat 1 cup granulated sugar, the olive oil, eggs, lemon zest, 1/4 cup lemon juice and the vanilla in a large bowl with a mixer on medium-high speed until combined and creamy, about 2 minutes. Reduce the mixer speed to low and beat in the flour mixture in three batches, alternating with the milk. Increase the mixer speed to medium high and beat until combined, about 1 minute.
Pour the batter into the prepared loaf pan and bake until the cake is golden brown and a toothpick inserted into the center comes out clean, 40 to 50 minutes. Transfer to a rack and let cool 40 minutes in the pan, then remove to the rack to cool completely.
Meanwhile, make the topping: Put the lemon slices in a small saucepan and cover with water. Bring to a boil, then drain. Return the lemon slices to the saucepan and repeat the boiling process two more times. Return the lemon slices to the saucepan and add 1 cup water, the remaining 3/4 cup granulated sugar and 2 tablespoons lemon juice. Bring to a boil, then reduce the heat so the liquid gently simmers; cook until the liquid is syrupy and the lemon slices are tender and translucent, about 15 minutes. Let cool completely.
Make the glaze: Combine the confectioners' sugar and 1 tablespoon lemon juice in a bowl until smooth, adding the remaining 1 tablespoon lemon juice if the glaze is too thick. Spoon the glaze over the cake, letting it drip down the sides. Remove the candied lemon slices from the syrup, letting the excess drip back into the saucepan. Arrange on top of the cake.
Photograph by Con Poulos
Courtesy of Food Network Magazine