Heat oven to 325 degrees. Prepare a 9x13 baking dish by spraying with cooking spray and set aside.
In a large bowl, combine the lemon zest and sugar and lightly rub together with your fingers or a fork until well combined. This helps release the oils in the zest which helps with the lemon flavor. Add in the eggs, oil, yogurt, lemon juice and vanilla. Mix together well using a spatula, whisk, or wooden spoon.
Stir in the dry ingredients with a wooden spoon or spatula until just combined.
Pour the batter into the prepared pan and bake for 30-40 minutes until a toothpick inserted in the center comes out clean or with moist crumbs. The middle should not be "jiggly" at all. It should be rounded and domed and cooked (use the toothpick to test).
While the cake is baking, whisk together the glaze ingredients until smooth and pourable. Let the cake rest for 10 minutes after baking and then pour the glaze over the warm cake.
You can serve this cake warm, at room temperature, or chilled. Store leftovers covered in the fridge. It will stay moist for several days.
I tried making this cake again using lemon yogurt and I would NOT recommend it. It sounds like a great idea but the artificial lemon flavor from the yogurt was all you can taste. Stick with plain yogurt, vanilla yogurt or even French vanilla yogurt.
You can use regular yogurt or Greek yogurt. I prefer using regular yogurt as I don't like the thicker, more sour flavor of Greek yogurt.