First you will make the lemon sugar. In a medium-sized food processor blend the granulated sugar and lemon zest for 30 seconds. Pour out the mixture into a bowl and set aside.
Next you will make the crumble. To that same food processor add 1 cup all-purpose flour, ¼ teaspoon of salt, ½ cup granulated sugar, and lemon zest. Blend until combined, about 10 seconds. While the food processor is on, add cubed butter, one piece at a time. Pulse into the mixture resembles wet sand. See notes below for more details. Add crumble mixture to a bowl, cover with saran wrap and refrigerate until needed.
Next you will make the batter! Preheat the oven to 350°. Grease and flour an 8-inch springform pan and set aside. In the bowl of a stand mixer beat room temperature butter and lemon sugar on medium-high speed until light and fluffy, between 3-5 minutes. Add in vanilla extract and eggs, and blend until just combined. Add flour, salt, baking powder and baking soda. On the lowest speed, pour in buttermilk and mix until the batter comes together. Do not over mix!
Pour the batter into the prepared pan and evenly spread in the pan.Right before it goes in the oven, remove the crumble from the fridge and sprinkle on top.
Bake for 40-45 minutes or until a toothpick inserted in the center comes out clean.Cool for 15 minutes in the pan before removing the springform sides. Let cool completed before glazing.
You will make the glaze while the cake is cooling. Use a whisk to beat together all of the ingredients for the glaze. Add more milk if you'd like the mixture to be thinner. Once the cake has completely cooled, drizzle the glaze on top and serve!