Heat the olive oil in a large pot over medium-high heat. Saute the garlic for about one minute, then add the white wine and cook until reduced by half, about one or two minutes. Add the tomatoes and use a wooden spoon to break them up into large pieces, then simmer, uncovered, for about five minutes.

Add the clams and toss to coat, then turn the heat to high, cover and cook for about 5 minutes. Remove the lid and use a pair of tongs to remove any clams that have opened up into a serving bowl. Continue placing open clams in the bowl until they've all opened up. If there are any clams that won't open, cover and wait a few minutes, and if they're still being stubborn, discard them.

Stir the butter into the sauce one piece at a time, then crumble in the blue cheese and stir. Some of the cheese will melt into the sauce, but be sure there are plenty of chunks that still remain. Stir in half of the basil, then pour over the clams. Top with the remaining fresh basil and serve immediately with crusty bread for dipping.