Combine garlic, basil, and 4 tablespoons of the olive oil in a blender. Process until a rough pesto forms.
Place tomatoes, just-made pesto, and red chile pepper in a small bowl and season with salt and pepper to taste. Lightly mash ingredients with a fork and set aside.
Cook the spaghetti. Meanwhile, toss the potatoes in with the remaining 2 Tablespoons of olive oil and arrange on a cookie sheet. Place under a preheated broiler until the potatoes are golden and crusty. Drain on paper towels.
When pasta is ready, drain and place in shallow pasta dishes (depending on what kind of a host you are: individual serving dishes or one large serving dish). Add the raw tomato-basil sauce and the hot potatoes. Toss well. Sprinkle with Parmesan and serve with extra cheese for the table.