In a medium saucepan, bring 4 cups of low-sodium vegetable broth to a gentle boil over medium heat. Gradually whisk in 1 cup of coarse yellow cornmeal, stirring constantly to prevent lumps. Once incorporated, reduce the heat to low and add 2 tablespoons of unsalted butter, stirring frequently for 20-25 minutes until the polenta thickens to a creamy consistency.

While the polenta cooks, preheat your oven to 425°F (220°C). On a baking sheet, toss 2 cups of halved ripe plum tomatoes with 2 tablespoons of extra-virgin olive oil, sea salt, and black pepper to taste. Arrange the tomatoes cut-side down and roast for 20-25 minutes, or until they become blistered and their skins are slightly charred.

Once your polenta is creamy, remove it from the heat and fold in 1 cup of freshly grated Parmesan cheese along with 1 tablespoon each of chopped fresh rosemary, thyme, and basil. Stir well until the cheese melts and the herbs are evenly distributed.

In a greased baking dish, pour half of the herbed polenta to create a smooth base layer. Evenly distribute the roasted tomatoes over this layer, ensuring they are well-spread. Top with the remaining polenta, smoothing it out gently.

Place the assembled dish under the broiler for about 5 minutes, or until the top is golden and slightly crispy. Watch closely to prevent burning.

Once removed from the oven, allow the dish to rest for 5 minutes before slicing and serving.