Dice tomatoes and place in a bowl. Season with salt. Add chopped garlic and diced onions.
Chiffonade the basil by stacking the leaves, rolling the stack of leaves lengthwise and slicing to create strips or ribbons of basil. Add them to the tomatoes.
Drizzle tomatoes with extra virgin olive oil and gently mix ingredients to combine. Add desired amount of grated cheese.
Cover mixture with plastic wrap and place bowl on top of a larger container filled with ice and let sit out on the counter 30-60 minutes before preparing crostini.