Combine the zucchini, scallions, flour, sugar, and salt in a medium mixing bowl. Toss to combine. Add the egg, lemon juice, and zest and stir until well incorporated.
Heat 1 tablespoon of olive oil and 1 tablespoon of butter (you can use more olive oil if keeping this recipe dairy-free) in a large cast iron skillet. Once the butter is melted and the oil is fairly hot, drop in the zucchini mixture in tablespoonfuls, making sure not to crowd the pan (about 5 at a time). Cook for about 1 minute on each side until browned and semi-firm. Remove to a paper towel to drain and repeat with the remaining zucchini mixture, adding more oil as necessary. NOTE: this can be done a day in advance. Simply reheat the cakes in a 350 degree oven for 10 minutes.
Serve with herbed Greek yogurt or aioli