Shred zucchini and place in colander to drain, pressing gently.
Preheat oven to 350 and add butter to 9 x 5 bread pan or baking dish to melt in the oven.
Add dry ingredients (first 4 ingredients) to large bowl and mix together with a spoon.
Before adding zucchini to the flour mixture, press gently on zucchini with paper towels to absorb excess liquid.
Add zucchini, basil, parmesan cheese, and 1 cup of the cheddar cheese to flour mixture and stir to incorporate. Reserve ½ cup of cheddar for the top.
Make a well in the center of the ingredients and add eggs. Mix eggs with a spoon or fork and then incorporate into a portion of the batter.
Add buttermilk and melted butter from the oven, leaving a bit of residual in the pan. Incorporate into the batter, but don't over mix.
Add batter to the preheated baking pan and top with remaining ½ cup of cheddar and more dry basil if desired.
Cook 55-60 minutes or until toothpick or thin knife inserted into the center comes out clean.
Let rest 5-10 minutes before removing from pan and slicing.