Warm the olive oil in a saucepan over medium heat, and add in the garlic to soften for about 2 minutes. Add in the tomato puree, cream and salt and whisk to combine. Once the tomato mixture begins to bubble, whisk in the goat cheese and half of the parsley until smooth.
Turn the heat off, and leave the pan over the warm burner. Whisk in the Cheddar thoroughly, and then do the same for the Fontina and the Parmesan. Taste the sauce, and stir in more salt if needed.
Toss the cooked pasta in the warm sauce, and spoon into bowls to enjoy immediately, topped with remaining parsley.