Heat the olive oil and saute the garlic a few minutes, just until softened. Keep the heat low so it doesn't brown at all.
Add the tomatoes. (If you use tomato puree you can probably skip the paste.) Add the paste if needed. Stir and cook 15-20 minutes, breaking up the tomatoes with the back of a wooden spoon.
Once it thickens, salt to taste and add the basil leaves. Stir and let cool while you make the pizzas.