Adjust oven rack to middle position and heat oven to 350 degrees.
Toss shallot with 1 teaspoon of EVOO in a bowl.
In a separate bowl, gently toss the tomatoes with remaining oil, garlic, vinegar, sugar, 1/2 teaspoon salt, 1/4 teaspoon pepper, and pepper flakes.
Spread tomato mixture in an even layer on a rimmed baking sheet, scatter shallot over tomatoes and roast until edges of shallot begin to brown and tomato skins are slightly shriveled, approximately 35t to 40 minutes. Do NOT stir tomatoes during roasting). Let cool for 5 to 10 minutes.
Meanwhile, bring 4 quarts of water to a boil in a large pot. Add pasta and salt and cook, stirring often, until al dente. Reserve 1/2 cup cooking water (optional), then drain pasta and return it to the pot.
Using a rubber spatula, scrape tomato mixture onto pasta. Add basil and toss to combine. Season with salt and pepper to taste and adjust consistency with reserved cooking water as needed.