Make the herb sour cream: Whisk the sour cream, chives and dill in a medium bowl. Set aside.
Make the zucchini cakes: Mix the zucchini, breadcrumbs, parmesan, basil, oregano, garlic, 1 teaspoon salt and 1/2 teaspoon pepper in a large bowl. In a medium bowl, whisk the eggs with the buttermilk, then stir the egg mixture into the zucchini mixture.
In a large skillet, heat the vegetable oil over medium heat. Working in batches, form patties with the zucchini batter (about 1/4 cup for each) and add to the skillet. Pan-fry the cakes until golden brown, 3 to 4 minutes per side. Drain on paper towels and sprinkle with 1 teaspoon salt. Serve while hot and crisp with the herb sour cream.