For the Chimichurri: In the bowl of a food processor, pulse parsley, cilantro, oregano, garlic, salt, and red pepper flakes until finely ground, about 30 seconds. Add olive oil and vinegar and pulse until just combined; season to taste with additional salt and vinegar.

In a large bowl, toss chicken thighs with honey and ⅓ cup of chimichurri to evenly coat. Refrigerate for at least 1 hour or up to 8 hours. Place remaining chimichurri in an airtight container; refrigerate until ready to use.

Line a 13-by-18-inch rimmed baking sheet with paper towels. Arrange cut zucchini in a single layer and sprinkle evenly with ¼ teaspoon salt. Let sit to allow zucchini to release excess moisture, about 15 minutes. Firmly pat dry with paper towels or a clean kitchen towel; set aside.

Adjust oven rack to upper third position of oven, about 6 inches below the heating element, and heat broiler to high.

Remove chicken from marinade; on a 13-by-18-inch rimmed baking sheet, space thighs out so there is plenty of space between them; discard marinade. Arrange zucchini, cherry tomatoes, red pepper, and onions around chicken. Drizzle vegetables with olive oil and season evenly with a pinch of salt.

Broil until chicken is dark golden brown and vegetables are just beginning to char, about 10 minutes. Using tongs, flip chicken and vegetables, and broil until vegetables are tender and chicken is lightly charred and measures 185°F (85°C) on an instant-read thermometer, 7 to 10 minutes.

Serve with reserved chimichurri, rice, flatbread, or roasted potatoes, if desired.