Bring a large pot of salted water to a boil, then add the pasta. Cook until just al dente, following package instructions, and then drain, setting aside.
Heat a tablespoon of olive oil in a deep pan over medium heat. Add the minced garlic and cook, stirring frequently, until fragrant and just golden, about 30 seconds.
Add the canned crushed tomatoes to the pan, stirring to combine with the garlic. Bring to a gentle simmer and cook for about 10 minutes, stirring occasionally, until the sauce thickens slightly and deepens in color.
Stir in the coconut milk, mixing well to create a smooth, velvety sauce. Let it simmer for another 2 minutes until heated through and slightly creamier, then season with salt and pepper to taste.
Once the sauce is ready, add the drained pasta directly into the pan. Toss gently to coat all the noodles evenly with the creamy tomato sauce, allowing the flavors to meld for about a minute.
Transfer the coated pasta to serving bowls, garnish generously with chopped fresh basil, and drizzle with a little extra olive oil if desired. Serve immediately while hot and fragrant.