Preheat an oven to 325 degrees F. Butter and flour a bundt pan. In a large mixing bowl, beat the butter and sugar with an electric beater until the mixture is pale and creamy, about 5 minutes. Beat in the lemon zest, lemon juice, and vanilla. Add the eggs, 1 at a time, beating until just combined after each addition. Fold in the flour and salt mixture in 2 batches, mixing after each addition until well combined. Be careful not to over mix. Spoon half of the batter into the bundt pan. Create a well in the batter and spoon in blueberry mixture. Take a butter knife and swirl blueberry sauce into batter. Top with the rest of the batter and swirl again. Bake for 45 to 55 minutes, or until a skewer poked into the cake comes out clean. Remove cake from oven and cool on a wire rack for 10 minutes.
In a small bowl combine powdered sugar and lemon juice. Stir until combined. Pour icing over cooled cake.
To make blueberry sauce:
Combine sugar, cornstarch, blueberries, lemon juice and zest in a small saucepan. Bring to a boil then reduce to a simmer for 20 minutes. Then pour mixture into a blender and blend on low for 30 seconds. Let cool before adding to cake.