Bring a large pot of salted water to a boil. Cook the pasta until al dente. Drain and let it cool slightly before mixing it with the other ingredients. This prevents mushy pasta.
Tear sourdough slices into small pieces. Toast them in olive oil with a pinch of salt over medium-low heat until golden and crunchy. Set aside.
Sauté garlic in olive oil for 1–2 minutes until fragrant. Remove from heat and toss in cherry tomatoes, white wine vinegar, oregano, salt, and pepper. Let them sit for at least 30 minutes to absorb flavors.
In a large bowl, mix the pasta with marinated tomatoes (including their juices), mozzarella, basil, half the croutons, and Parmigiano. Toss gently to coat everything evenly.
Serve in a wide bowl or platter. Drizzle with balsamic glaze, sprinkle the remaining croutons, and top with extra Parmigiano.