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.