Bring a large pot of generously salted water to a boil. Cook the pasta according to the package directions until al dente. Before draining, reserve about ½ cup of the pasta water.
While the pasta cooks, heat the olive oil in a large skillet over medium-low heat. Add the garlic and gently cook for 1–2 minutes, stirring frequently, until fragrant. Keep the heat moderate so the garlic does not brown or become bitter.
Stir in the tomato paste and cook for about 1 minute, allowing it to deepen in color and develop a richer flavor.
Pour in the crushed tomatoes and add the salt, black pepper, Italian seasoning, and red pepper flakes if using. Stir well and bring the sauce to a gentle simmer.
Let the tomato sauce cook uncovered for 10–12 minutes, stirring occasionally, until it thickens slightly and the flavors come together. If the tomatoes taste particularly acidic, stir in the optional sugar.
Tear or roughly chop half of the fresh basil and stir it into the sauce during the final 2 minutes of cooking. Reserve the remaining basil for serving.
Add the drained pasta directly to the skillet and toss well to coat every strand or piece with the tomato sauce.
Add a splash of reserved pasta water if the sauce seems too thick. Toss for another minute until the sauce becomes glossy and clings to the pasta.
Taste and adjust the seasoning with additional salt, black pepper, or red pepper flakes as needed.
Divide the pasta between bowls and top with the remaining fresh basil and vegan Parmesan, if using. Finish with a small drizzle of extra-virgin olive oil and serve immediately.