In a medium saucepan, bring 4 cups of vegetable broth to a gentle boil over medium heat. Gradually whisk in 1 cup of cornmeal, ensuring there are no lumps. Once combined, reduce the heat to low and cook for 20-25 minutes, stirring continuously until the mixture thickens and becomes creamy.

While the polenta is cooking, preheat your oven to 425°F (220°C). Halve 2-3 ripe plum tomatoes and toss them in a bowl with olive oil, salt, and pepper for flavor. Spread the tomatoes cut-side down on a parchment-lined baking sheet, then roast for 20-25 minutes.

Once the polenta is cooked, stir in 2 tablespoons of butter and your chosen chopped fresh herbs, mixing well to infuse the flavors. Spread the herbed polenta evenly in a greased baking dish. Layer the blistered tomatoes on top and drizzle with a bit more olive oil.

Place the assembled dish under the broiler for 3-5 minutes, keeping a close eye to prevent burning. You want the top to become golden and slightly bubbly.

After broiling, remove the dish from the oven and let it rest for about 5 minutes to set the layers. Slice the polenta bake into squares, and garnish with basil leaves. Serve warm.