Line a sheet pan with foil. Toss tomatoes and garlic with oil and wine. Season with salt and pepper and sprinkle sugar. Toss with herbs. Spread out in one layer. Roast in oven for about 40 minutes-1 hour until tomatoes are tender. Pick out herb stems but leave in leaves. Transfer sauce to a large serving bowl. Add a drizzle of olive oil.
Bring a pasta pot of water to a boil. Add a generous couple of pinches of salt. Boil pasta until al dente. Add 1-2 ladlefuls of pasta water to sauce. Reserve 1/2 cup water. Drain pasta and add to bowl with sauce. Stir to coat. Add a little more olive oil or pasta water to moisten if needed. Dust lightly with grated cheese. Pass grated cheese at table for individual servings.