Preheat oven to 325 degrees F. Grease and flour a 10-cup bundt pan.
In a large bowl, mix the flour, baking soda and salt.
In the bowl of a mixer, cream together the butter and sugar until light and fluffy. Add the eggs, one at a time, until they are fully incorporated. Add vanilla.
Add the flour mixture in two additions, alternating with the lemon pudding. Add lemon zest. Continue beating for about 4 minutes, scraping sides occasionally, until the batter is shiny.
Pour batter into prepared pan and bake for 50 minutes to an hour, until a skewer comes out clean.
Allow the cake to cool in the pan for 10 minutes then unmold onto the rack rounded side up.
For the glaze, whisk together the powdered sugar, lemon zest and lemon juice, starting with half the lemon and adding more untilthe desired consistency is reached.
Place the cake on the serving platter and drizzle with the glaze.