Cut potatoes into 1 1/2- to 2-inch chunks and spread level in a shallow 3 quart casserole (9 by 13 in.). Bake in a 425 degrees oven for 20 minutes.
In a blender or food processor, combine tomatoes (with juice), garlic, basil, lemon juice, and oil. Whirl until smooth.
Pour tomato mixture over potatoes and continue to bake until potatoes are tender when pierced, 20 to 25 minutes longer; stir several times.
Sprinkle with more basil and/or Parmesan cheese; season to taste with salt and pepper.
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