1. Preheat oven to 350deg F/180deg C/Gas 4. Butter and flour two loaf pans and set aside.
2. In a medium sized bowl, sift together flour, cornmeal, salt, baking powder and baking soda. Set aside. Set the four eggs out on the counter to come to room temperature while you beat the butter and sugar.
3. In the bowl of a stand mixer, beat butter on medium speed until softened and pliable. Add the sugar and beat until light and fluffy, about 4 minutes. Add the avocado and beat another minute to incorporate. Scrape down the sides of the bowl to ensure that everything is thoroughly mixed.
4. Add the eggs one at a time, beating 1 minute after the addition of each egg. Beat in vanilla extract.
5. Reduce the mixer speed to low and add half of the flour mixture, all of the buttermilk, and then the rest of the flour mixture. Beat just until combined.
6. Divide the dough between the two loaf pans and place in the oven. Turn the oven down to 325deg F/170deg C/Gas 3. Bake for 40-45 minutes or until a skewer inserted in the center of the cakes comes out clean. Let cool in the pan for 10 minutes, then invert onto a cooling rack to cool completely.