Wash and cut the tomatoes into similar-sized pieces. If you are using cherry tomatoes, you can leave them whole.
Heat the olive oil in a tall saucepan over medium low heat. Add the garlic and anchovies, and cook them for 1 to 2 minutes over medium-low heat, until the anchovies dissolve and the garlic starts to sizzle.
Carefully add the tomatoes to the pot, together with the salt and chili pepper, and mix everything together.
Let the soup cook for 45 to 50 minutes, stirring occasionally. At this point, the tomatoes should be completely wilted and fallen apart into a nice soup.
Remove the pan from the heat, and carefully pass the soup through a mesh strainer to discard the tomato skins and seeds.
Pour the soup back into the pan to reheat it, then add the basil. Taste the soup and adjust the salt and chili pepper, if needed.
Once the soup is hot, serve it with a drizzle of olive oil on top, the bread, and the cheese.