Bring a large pot of salted water to a boil and cook the pasta until just al dente, then drain, reserving a cup of pasta water.
Meanwhile, heat olive oil in a deep skillet over medium heat until shimmering and warm to the touch.
Add the finely minced garlic to the oil and cook for about 30 seconds, until fragrant and slightly golden, stirring constantly to prevent burning.
Sprinkle the red pepper flakes into the garlic and toast for about 15 seconds, releasing their spicy aroma and turning the flakes a darker red.
Pour in the crushed tomatoes, stirring well to combine and scraping up any bits stuck to the pan. Bring the sauce to a gentle simmer.
Let the sauce simmer uncovered for 10-12 minutes, stirring occasionally, until it thickens slightly and turns a rich, vibrant red.
Season the sauce with salt, tasting and adjusting as needed. If the sauce becomes too thick, stir in a splash of reserved pasta water to loosen it.
Add the cooked pasta directly into the sauce, tossing to coat evenly and allowing the flavors to meld over low heat for 1-2 minutes.
Remove from heat, tear fresh basil leaves over the pasta, and toss gently to distribute the herbal aroma.
Serve immediately, garnished with extra basil and a drizzle of olive oil if desired. Enjoy the glossy, spicy, and fragrant vegan arrabbiata hot from the pan.