Pasta with Grilled Tomato and Scallion Sauce

Light a grill and preheat for at least 10 minutes or preheat a grill pan. Oil the grates. Meanwhile, soak 1 bamboo skewer for 10 minutes. Thread the garlic on the skewer. Brush the scallions and the cut sides of the tomatoes with olive oil and season with salt and pepper. Grill the garlic and scallions over high heat, turning frequently, until blistered in spots and softened, about 2 minutes. Grill the tomatoes cut side down until nicely charred, about 2 minutes. Flip and grill until the skin starts to shrink, about 1 minute. Peel the garlic and finely chop, then transfer to a large bowl. Thinly slice the scallions crosswise and transfer to the bowl. Pull off the tomato skins, dice the tomatoes and add them to the garlic and scallions. Meanwhile, in a large pot of boiling salted water, cook the pasta until al dente. Reserve 1/2 cup of the pasta water and drain. Add the hot pasta, the cheese and the 2 tablespoons of olive oil to the tomatoes and toss. Add the pasta water, little by little, if you need to loosen the sauce. Season the pasta with salt and pepper and serve immediately.