Prepare the Zucchini: Toss the grated zucchini with ½ teaspoon of salt in a colander. Let it sit over the sink (or in a bowl) for 10 minutes to drain excess moisture.
Mix the Dry Ingredients: In a large bowl, whisk together the cornmeal, flour, baking powder, baking soda, cumin, and remaining ½ teaspoon of salt.
Combine the Batter: In a separate bowl, whisk the eggs with the melted butter. Gradually add this to the dry ingredients, forming a thick batter. Squeeze out as much moisture as possible from the salted zucchini and fold it, along with the scallions and garlic, into the batter.
Cook the Fritters: Heat a large skillet over medium heat with enough olive oil to coat the bottom. Drop 2-tablespoon portions of the batter into the skillet, flattening each slightly. Fry until golden brown, 3 to 4 minutes per side. Drain on a paper towel-lined plate, sprinkling with salt while still hot. Repeat with the remaining batter.
Make the Mint Chutney: In a blender, combine mint, cilantro, jalapeño, garlic, lime juice, shallot, salt, and 2 tablespoons of water. Blend until smooth, adding more water a tablespoon at a time if needed.
Serve: Plate the zucchini-cornmeal cakes alongside the mint chutney and a dollop of yogurt.