Preheat the oven to 400°F (200°C). In a bowl, toss the halved cherry tomatoes with olive oil, salt, pepper, and balsamic vinegar. Spread them on a baking sheet and roast for 20-25 minutes until caramelized.

In a saucepan, bring the vegetable broth to a boil. Gradually whisk in the polenta, stirring constantly to avoid lumps. Reduce heat and cook for about 15-20 minutes until thickened. Stir in parmesan cheese, olive oil, oregano, basil, salt, and pepper.

In a greased baking dish, spread half of the polenta mixture evenly. Layer the roasted tomatoes on top, then add the remaining polenta. Top with shredded mozzarella cheese.

Bake in the preheated oven for 15-20 minutes until the cheese is bubbly and golden. Remove from oven and let it cool slightly before serving.

Garnish with fresh basil and serve warm. Enjoy your savory herbed polenta and roasted tomato bake!