Bring a large pot of salted water to a rolling boil over high heat. Add gluten-free fettuccine and cook according to package instructions, usually about 8–10 minutes, until al dente. Drain the pasta in a colander and set aside, reserving some pasta water.

In a large skillet, heat a splash of water, vegetable broth, or oil over medium heat. Add minced garlic and chopped sun-dried tomatoes, stirring for about 2 minutes until fragrant and slightly softened.

Sprinkle in Italian seasoning, balsamic vinegar, and tomato paste. Cook for 2–3 minutes, stirring frequently until well combined and aromatic.

Fold in the cherry tomatoes and water or vegetable broth into the skillet. Cover and simmer for 3–4 minutes until tomatoes soften and burst. Smash some of the cherries against the skillet.

Reduce heat to low, stir in thick coconut milk and nutritional yeast. Mix thoroughly, season with salt and pepper to taste. Simmer gently for 5–10 minutes until it thickens.

Add the drained fettuccine and arugula to the skillet with the creamy sauce. Toss gently until pasta is evenly coated and arugula wilts slightly. Add reserved pasta water if sauce is too thick.

Transfer the creamy vegan sun-dried tomato pasta to serving bowls. Garnish with chopped flat-leaf parsley and sprinkle with vegan parmesan if desired.