Move an oven rack to the middle position and preheat oven to 350 degrees. Coat a 9-inch loaf pan with nonstick spray and line with parchment paper
In a medium bowl, whisk together the flour, baking powder, and salt. Set aside.
In a large bowl, whisk together 1 cup sugar, yogurt, eggs, lemon zest, and vanilla. Add the dry ingredients in batches, whisking to incorporate after each addition. Fold in oil and stir carefully until uniformly combined. Pour into prepared pan.
Bake until a toothpick inserted comes out clean with a few crumbs attached, about 50-60 minutes. The cake should be fragrant and spring back when pressed lightly. Remove from oven and cool in pan 10 minutes.
Meanwhile, in a medium bowl, stir together powdered sugar, lemon juice, lemon zest (if using) until smooth.
Using a sharp knife, slice around the inside of the cake pan to loosen the cake. Flip out onto a large plate. Slowly drizzle glaze over the top. Cool cake completely. The glaze will harden in 20 to 30 minutes.
Notes
Baking powder: Instead of yeast, quick breads such as loaf breads, muffins, biscuits, and scones use chemical leavening agents, in this case baking powder (baking soda is another example).
Yield: 1 loaf cake makes about 8 slices.
Storage: Store covered at room temperature for up to 4 days.
Order of operations: The lemon glaze can be made while the cake is baking. Leave the glaze at room temperature.
More glaze: To make a second glaze for the loaf cake (in addition to the one outlined above), whisk 2 tablespoons lemon juice and 1 cup powdered sugar. Drizzle over cooled cake.
Blueberries: You can add 6 ounces fresh or 1 cup frozen blueberries to make a Blueberry Lemon Yogurt Cake. If using frozen blueberries, leave them frozen right up until the moment you are going to stir them in. Then, fold them in with as few strokes as possible. If you do see some residual purple streaks in the batter, they likely won't bake up that way. In my experience, the cake looks the same as one made with fresh blueberries.