Prepare a grill for medium-high heat (550–600°F). Cut each zucchini in half lengthwise, then score the cut sides in a ¼-inch crosshatch pattern, going as deep as possible without cutting through the skin. Spray or toss the zucchini with olive oil and 1½ teaspoons salt in a large baking dish or on a rimmed baking sheet. Let sit at least 15 and up to 30 minutes.
Meanwhile, combine the parsley, cilantro, mint, shallot, garlic, jalapeño, lime juice, fish sauce, sugar, and 1 teaspoon salt in a food processor. Pulse until finely chopped. Scrape the mixture into a medium bowl, pour in the ½ cup olive oil, and stir to incorporate. Taste and adjust seasoning if needed. The chimichurri can be made up to 4 hours in advance and stored covered at room temperature.
Brush or spray the corn lightly with olive oil and grill until charred on all sides, about 5 minutes total. Remove to a cutting board. When cool enough to handle, cut the kernels from the cob and fold into the chimichurri.
Grill the zucchini, cut sides down, until well charred underneath, about 5–7 minutes. Transfer to a cutting board and let cool slightly. Slice crosswise on a diagonal into 3 or 4 pieces.
Spread about ½ cup of the chimichurri over a platter. Arrange zucchini on top and spoon more chimichurri over. Garnish with additional chopped herbs, if desired. Serve remaining chimichurri on the side.
