This uncomplicated yet exquisite dish calls for a visit to a fresh pasta shop, or make your own pasta from your favorite recipe. You’ll want a supple canvas to convey the sauce’s delectable flavors.
Preheat oven to 425F. Quarter tomatoes lengthwise, remove their seeds, and cut wedges in half. Gently toss in a bowl with 2 tablespoons olive oil, 1 teaspoon garlic, and basil. Place tomatoes on baking sheet. Roast until beginning to dry and wrinkle, about 20 minutes.
In a large skillet, heat the remaining 2 tablespoons olive oil over medium heat. Add onion and remaining 1 tablespoon garlic and cook until translucent. Add wine and reduce by four-fifths. Add cream and reduce by one-half. Stir in lemon juice and horseradish. Season with salt, pepper, and sugar.
Cook pasta in a large pot of boiling salted water until tender but firm, 1 to 2 minutes for fresh, depending on thickness, or 9 to 12 minutes for dried. Drain and transfer to a large warmed serving bowl. Add sauce and toss. Divide among plates, drizzle with basil oil, and top with roasted tomatoes. Garnish with Parmesan shavings.