In a large bowl, combine tomatoes, salt, garlic, olive oil, and the roughly-chopped basil.
Allow the mixture to chill for 15 minutes in the refrigerator. While your topping is cooling, lightly grill your biased-cut baguette. If you don’t have a grill or griddle available, try toasting them in a sauté pan until they get brown and crispy.
To assemble, place your baguette slices on a large plate and top with the chilled tomato mixture.
Then place the Parmesan cheese on top and garnish with the leftover fresh basil.