This cake is fluffy, supremely moist and has a grown-up vibe about it: not kiddie stuff. The buttermilk in the cake adds even more tang and is essential to the rise and delicate crumb.
Heat the oven to 350 degrees. Grease a 9-by-13-by-2½-inch metal baking pan with baking spray.
In a medium bowl, whisk together the flour, baking powder, baking soda and salt. In a large bowl, whisk together the sugar, oil, buttermilk, lemon zest and juice and eggs until smooth. Add the dry ingredients to the liquid ingredients and whisk until just combined. Pour the batter into the prepared pan and smooth the top. Bake until golden brown on top and a toothpick inserted in the center of the cake comes out clean, 35 to 40 minutes.
While the cake is in the oven, make the syrup and glaze: In a small bowl, whisk together 1/4 cup powdered sugar and 3 tablespoons lemon juice until they form a thin syrup. In a medium bowl, whisk together the remaining 1 cup plus 2 tablespoons powdered sugar and 2 teaspoons lemon juice, the butter and milk until they form a thicker, smooth glaze.
Remove the pan from the oven and let the cake cool for 5 minutes. Using a toothpick or the tines of a fork, poke the cake all over. Slowly drizzle the syrup evenly over the cake and let the cake cool completely.
Scrape the glaze onto the cake and use a spoon to spread it evenly over the top. Scatter more lemon zest over the cake, if you like, to garnish. Let the cake stand for 10 minutes to set the glaze before serving from the pan.
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