In a large heavy-bottomed pot or Dutch oven, heat the olive oil over medium heat.
Add the garlic and cook until fragrant but not browned, 1 to 2 minutes. Add the tomatoes, bring to a simmer, and cook until thickened slightly, about 15 minutes. Stir in sugar, and season with salt, to taste.
Meanwhile, cook pasta in boiling, salted water until al dente. Drain.
Serve sauce over hot pasta with a drizzle of olive oil, a sprinkle of basil, and cheese.
Let extra sauce cool completely and then seal in airtight containers. Refrigerate for up 1 week and freeze for up to 1 month.