Pour the polenta into a saucepan and cover it with ¾ cup cold water. Let it stand for 5 minutes to allow the grains to begin absorbing the liquid and soften slightly.
Add 2½ cups of boiling salted water to the pan and return it to a boil over medium-high heat. Stir continuously for 10–15 minutes until the polenta becomes smooth, creamy, and thickened, with no lumps remaining.
Lightly sprinkle a baking sheet with water to prevent sticking. Stir the butter into the hot polenta until it's fully incorporated and glossy, then spread the mixture evenly across the prepared baking sheet in a layer about ½ inch (1cm) thick. Set aside and let it cool completely until firm.
In a bowl, whisk together all the marinade ingredients. Add the zucchini, tomatoes, fennel, and onion to the marinade, tossing to coat everything thoroughly. Cover the bowl and refrigerate for 30 minutes to let the vegetables absorb the flavors.
Remove the vegetables from the marinade, shaking off any excess liquid, and place them on a preheated hot grill. Cook for 2–3 minutes on each side until they're charred and tender. Meanwhile, cut the cooled, firm polenta into strips or wedges. Brush each piece generously with melted butter and grill for 1–2 minutes per side until golden brown with attractive grill marks.
Arrange the grilled vegetables and polenta strips on a serving platter and serve immediately while hot, perhaps with an extra drizzle of the marinade or fresh herbs as garnish.