Heat the olive oil in a large pot over medium heat. Add the onion, garlic, bay leaf, and Italian seasoning and cook, stirring, until the onion is softened, 4 to 5 minutes.

Add the diced tomatoes, chicken broth, and 2 cups of water to the pot. Increase the heat to high and bring to a boil. Add the pasta, return to a boil, and cook until the soup is slightly thickened and the pasta is al dente, 8 to 10 minutes. Remove from the heat and stir in the chicken. Discard the bay leaf. Season with salt and pepper.

Divide the soup among bowls and top with the mozzarella. Let the cheese melt for 1 minute. Top with chopped basil, Italian seasoning, and red pepper flakes, if you like.