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Preheat oven to 350 degrees. Grease a 9x5x3" loaf pan.
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In a small saucepan, brown the butter over median-high heat, (The butter should sizzle, foam, and then the foam and sizzle should subside. It should smell fragrantly nutty). Allow to cool.
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Trim the ends from the zucchini. Slice 5-7 super thin discs off, and set aside. Coarsely grate the remaining zucchini.
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In a bowl, stir together the flours, cornmeal, sugar, baking powder, baking soda, and salt; set aside.
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In the bowl of an electric mixer fitted with the paddle attachment, combine the browned butter, the eggs, and buttermilk; mix to combine. Add in the zucchini and green onion, and mix to combine. Add in the flour mixture, and mix on low until just combined.
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Pour the batter into the prepared pan and smooth the top. Place the reserved zucchini discs along the center of the batter the garnish. Bake for 55-65 minutes, until golden and a knife or toothpick inserted into the center comes out clean. Allow to cool completely in the pan before removing and slicing.