In a bowl, cover tomatoes with boiling water. Let stand until soft, 10 to 15 minutes.
Meanwhile, in a 6- to 8-inch frying pan over medium heat, stir pine nuts until golden, about 5 minutes.
Drain tomatoes; squeeze out and discard excess liquid. In a food processor, whirl tomatoes, nuts, cheese, basil, and garlic until finely chopped. (Or with a knife, mince tomatoes, nuts, basil, and garlic; put in a bowl and mix in cheese.) Add salt and pepper to taste.