Preheat your oven to 375°F (190°C).
Wash and cut the ripe tomatoes in half. Using a box grater or a handheld grater, grate the tomatoes into a bowl, with the skin left behind.
To the grated tomatoes, add the crushed garlic, chopped basil, grated Parmesan cheese, and season with salt and freshly ground black pepper to taste.
Stir all the ingredients together until they are well combined. The mixture should have a rich tomato aroma and be well-seasoned.
Slice the fresh baguette into rounds, approximately 1/2 inch (1.3 cm) thick.
Place the baguette slices on a baking sheet, drizzle with some olive oil and toast them in the preheated oven for about 5 minutes or until they are lightly golden.
Remove the toasted baguette slices from the oven and let them cool slightly. Then, generously spoon the tomato mixture onto each slice.
You can drizzle extra virgin olive oil over the tomato-topped baguette slices. As well as garnish with additional fresh basil leaves if desired.